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How to know if a Date object represents only Time in Java?

I'm trying to save data about date and time to List. Let's say, I have List<Date>. I have 2 types of formatting of strings: dd/mm/yy and hh:mm. Well, I'm able to easily format and create an instance of java.util.Date using SimpleDateFormat. However, when I try to print the object, the one that I saved time data into prints something like this:
Thu Jan 01 06:30:00 AZT 1970
How do I differentiate between these two and get the following output instead:
06:30
Note: Years may start earlier than 1970.
Thanks for the help and appreciate the effort.

How to know if a Date object represents only Time in Java?
There is no way to do this reliably. Every value of Date that you are using to represent a time also represents a valid date. And you can't distinguish the two cases ... except by using an unreliable heuristic.
The real problem is that you should not use Date to represent times.
A Date represents a single point in the time continuum.
A time is either a duration or multiple time points depending on how you use it. (It depends on your use-case.)
In fact, you probably not be using java.util.Date at all. Date is legacy Java class that has many API flaws. It was superseded in Java 8 by the classes and interfaces in the java.time package. These provide distinct classes for the various different concepts.
I recommend that you read the Date-Time trail in the Oracle Java Tutorial to get a basic understanding. This will help you decide the correct classes to choose for your use-case.
Time is complicated in the real world, and it is complicated in Java too.

How can I parse RFC 3339 date string into ZondeDateTime?

Problem:
I should parse an RFC3339 date string. It works fine with ISO_ZONED_DATE_TIME:
ZonedDateTime.parse("1985-04-12T23:20:50.52Z", ISO_ZONED_DATE_TIME);
ZonedDateTime.parse("1996-12-19T16:39:57-08:00", ISO_ZONED_DATE_TIME);
Let's say I'll fix a problem of Unknown Local Offset Convention just to not accept these dates.
But I still have a problem with some corner cases like this:
1990-12-31T23:59:60Z
This represents the leap second inserted at the end of 1990.
1990-12-31T15:59:60-08:00
This represents the same leap second in Pacific Standard Time, 8
hours behind UTC."1990-12-31T15:59:60-08:00"
Question:
How can I parse it avoiding to lose any seconds?
Update:
Does it exist any alternative to ZonedDateTime that suits well
RFC3339?

java.time doesn’t offer any direct support for what you want. Just earlier today I wrote this answer that also has a section on parsing a leap second. But what is said there is all there is.
So there’s hand parsing left. I’d try something along these lines: Use a regular expression for detecting whether the second is 60. If so: Substitute it with 59. Parse. Convert to UTC. If the time of day in UTC is 23:59:59, assume there was a valid leap second in the original string; otherwise the string didn’t denote a valid time.
I suggest that in case of a leap second second values up to 60.999999999 are valid. So to detect whether there is a 60 you need to look at what comes after the colon (if any) after the minutes, and not depend on whether there is a fractional part too.

(Re)Use DateTimeFormatter for parsing date ranges or mix DateTimeFormatter with regex

I have the following String representing a date range which I need to parse:
2018-10-20:2019-10-20
It consists of 2 ISO date strings separated by :
The string can get more complex by having repeated date ranges mixed with other text. This can be done by a Regex.
However, given that the latest Java has Date/Time support that most coders here and elsewhere are ecstatic about, is it possible to use, say, LocalDate's parser or a custom DateTimeFormatter in order to identify the bits in my String which are candidates for ISO-date and capture them?
Better yet, how can I extract the validation regex from a DateTimeFormatter (the regex which identifies an ISO-date, assuming there is one) and merge/compile it with my own regex for the rest of the String.
I just do not feel comfortable coding yet another ISO-date regex in my code when possibly there is already a regex in Java which does that and I just re-use it.
Please note that I am not asking for a regex. I can do that.
Please also note that my example String can contain other date/time formats, e.g. with timezones and milliseconds and all the whistles.

Actually, DateTimeFormatter doesn't have an internal regex. It uses a CompositePrinterParser, which in turn uses an array of DateTimePrinterParser instances (which is an inner interface of DateTimeFormatterBuilder), where each instance is responsible for parsing/formatting a specific field.
IMO, regex is not the best approach here. If you know that all dates are separated by :, why not simply split the string and try to parse the parts individually? Something like that:
String dates = // big string with dates separated by :
DateTimeFormatter parser = // create a formatter for your patterns
for (String s : dates.split(":")) {
parser.parse(s); // if "s" is invalid, it throws exception
}
If you just want to validate the strings, calling parse as above is enough - it'll throw an exception if the string is invalid.
To support multiple formats, you can use DateTimeFormatterBuilder::appendOptional. Example:
DateTimeFormatter parser = new DateTimeFormatterBuilder()
// full ISO8601 with date/time and UTC offset (ex: 2011-12-03T10:15:30+01:00)
.appendOptional(DateTimeFormatter.ISO_OFFSET_DATE_TIME)
// date/time without UTC offset (ex: 2011-12-03T10:15:30)
.appendOptional(DateTimeFormatter.ISO_LOCAL_DATE_TIME)
// just date (ex: 2011-12-03)
.appendOptional(DateTimeFormatter.ISO_LOCAL_DATE)
// some custom format (day/month/year)
.appendOptional(DateTimeFormatter.ofPattern("dd/MM/yyyy"))
// ... add as many you need
// create formatter
.toFormatter();
A regex to support multiple formats (as you said, "other date/time formats, e.g. with timezones and milliseconds and all the whistles") is possible, but the regex is not good to validate the dates - things like day zero, day > 30 is not valid for all months, February 29th in non-leap years, minutes > 60 etc.
A DateTimeFormatter will validate all these tricky details, while a regex will only guarantee that you have numbers and separators in the correct position and it won't validate the values. So regardless of the regex, you'll have to parse the dates anyway (which, IMHO, makes the use of regex pretty useless in this case).

Regex + Date Parser is the right option.
You have to write regex yourself, since the date parser is not using regex.
Your choice if regex can be simple, e.g. \d{2} for month, and let the date parser validate number range, or if it has to be more strict, e.g. (?:0[1-9]|1[0-2]) (01 - 12). Range checks like 28 vs 30 vs 31 days should not be done in regex. Let the date parser handle that, and since some value ranges are handled by date parser, might as well let it handle them all, i.e. a simple regex is perfectly fine.

Best way to store time in java, in format of HH:MM

After doing my research I wasn't able to find a method or data type that should be used for variable in order to store time in format of HH:MM, I did find methods to get this from a string like "14:15:10", but I think this is not the best way, as I'll need to add or subtract from time. I tried doing this as a double, but ran into following issue, when you have a time like 05.45 stored and add 0.15 (or 15 minutes) to it, the result is 05.60 where as with HH:MM format you'd expect it to be 06.00.
I'm looked through java documentation and still am, but can't seem to find any way to achieve this, closest I got to is date format like dd/mm/yyyy hh:mm:ss

Use Joda Time. It provides much better operations to do date/time manipulation than standard java dates. If you want to use internal JDK classes, use java.util.Date.

Since Java 8, you can use the new API for dates and times, including Instant, ZonedDateTime and LocalDateTime. This removes the use for the third party library Joda time. It also makes calculations more easy and correct. The advice below is a bit dated but still has some good points.
—————
What you definitely should NOT do is store them in your own custom format. Store the Long value that represents the Unix Epoch.
A DateTime is nothing more than a number to a computer. This number represents the amount of seconds (or milliseconds) since 1970-01-01 00:00:00 UTC. It's beyond the scope of this answer to explain why this date was universally chosen but you can find this by searching for Unix Epoch or reading http://en.wikipedia.org/wiki/Unix_time.
This also means there is NO timezone information stored in a DateTime itself. It is important to keep this in mind when reasoning about dates and times. For things such as comparing DateTime objects, nothing concerning localization or timezones is done. Only when formatting time, which means as much as making it readable to humans, or for operations such as getting the beginning of the day, timezones come into play.
This is also why you shouldn't store the time like 20:11:15 in a string-like format because this information is meaningless without timezone information. I will give you 1 example here: Consider the moment when the clock is moved back 1 hour, such as when moving away from daylight savings time. It just happened in a lot of countries. What does your string 02:30 represent? The first or the second one?
Calculations such as subtraction are as easy as doing the same with numbers. For example: Date newDate = new Date(date1.getTime() - date2.getTime());. Or want to add an hour to a date? Date newDate = new Date(oldDate.getTime() + 1000 * 60 * 60);
If you need more complex stuff then using Joda time would be a good idea, as was already suggested. But it's perfectly possible to just do even that with the native libraries too.
If there's one resource that taught me a lot about date/time, it would be http://www.odi.ch/prog/design/datetime.php

Java has java.sql.Time format to work with time-of-day values. Just import it and create variables.
import java.sql.Time;
//now we can make time variables
Time myTime;
Just saw it on https://db.apache.org/derby/docs/10.4/ref/rrefsqlj21908.html

The answer that is right for your case depends on what you want to do.
Are you using a RDBMS as your persistence engine?
If so, are you already working with legacy data formats or are you building a database from the ground up?
Are you simply storing this data, or will you be doing extensive date arithmetic and/or precedence calculations?
Are you in one time zone or do you need to work with time instants across many time zones?
All of these things are important and factor into your decision of how to represent your times and dates.
If your needs require a lot of date arithmetic (eg. determining days between dates) or sorting based on timestamps, then consider using a floating point date format. The advantage of using a numeric format for timestamps is that doing date arithmetic and comparison/sorting operations becomes trivial; you merely do simple arithmetic. Another advantage is that floats and longs are primitive data types. They do not need to be serialized, they are already extremely lightweight, and everything you need to use them requires no external dependencies.
The main disadvantage to using numeric formats for timestamps is that they are not human friendly. You'll need to convert them to and from a String format to allow users to interact. Oftentimes, this is worth the effort. See: How do I use Julian Day Numbers with the Java Calendar API?
I recommend that you consider storing timestamps as Julian Day Numbers (JDNs) or Modified Julian Day Numbers (MJDs). Both will represent dates and times to millisecond precision using an 8 byte float. Algorithms for converting to and from display formats for both of these are highly standardized. They confer all the advantages of using numeric dates. Moreover, they are defined only for GMT/UTC which means that your timestamps are already universalizable across time zones right out of the box (as long as you localize properly).

If you dont want the full date object, your best bet is to store it in a string, but I personally would still recommend date as it also contains a lot of convenient methods that will come in handy. You can just get the time as a whole from a date object and ignore the rest.

In terms of "storing" a date, you should use a long. This is how the system sees it and how all calculations are performed. Yes, as some point out you will eventually need to create a String so a human can read it, but where people run into trouble is when they start thinking of a date in terms of format. Format is for readability, not for calculations. java.util.Date and java.util.Calendar are fraught with issues (Effective Java, Bloch, et. al. has plenty to say about it) but are still the norm if you need handy date operations.

Is there any way to convert date String of any format to millisecond in java?

Is there any function or library which gets a date in milliseconds, given a String?
This question shows how to convert a formatted String to a Date object, but is there any way to do this with an unformatted String?

Basically, the task is impossible. Here's an example:
01/04/2012
In the US, that means January 4th 2012. In Australia, that mean 1st April 2012.
Without knowing where you are and what date formats conventionally mean, it is impossible to accurately map an arbitrary date-like string to a date time value that matches what the user actually meant.
And even if you do know about the relevant local conventions, users have a remarkable propensity to be oblivious to ambiguity. Dealing with that may require deep domain knowledge (or mind reading skills!) to disambiguate the possible meanings.
When you think about it, this is why modern user interfaces typically use a date-picker widget of some kind when the user needs to enter a date / time

first convert the string to Date. From there you can get time in milis using Date.getTime() method