Develop Reference

Is it possible to know the app which is opened currently?

I am a beginner in android development. I want to know that is it possible to know the app which is opened currently. I came to know that finding the apps which are running currently through Activity Manager (getRunningTasks()) is now removed from the Android studio. So I want to know is there any other way to know? I just want to know the app which is opened and running currently on the mobile but not the apps running in the background Could somebody please help me in this case?

You can use AccessibilityService to get event notification. But AccessibilityService are specifically for accessibility uses. If you use the service for other purposes, then the application will more likely to be downed/removed for PlayStore due to policies. Another viable option is UsageStatsManager, but with some limitations.
UsageStatsManager is not push event based system. You have to poll in few mills(depends upon the use-case)
Usage Access Permission grant/deny is not straight forward. You have to start Setting Activity with Settings#ACTION_USAGE_ACCESS_SETTINGS action and have to rely on the users understanding of how to grant permission(Since permission list may contain other applications).

Getting user behavior on the Android Phone (App History, Browse History etc)

Is it possible to get the user behavior on the phone (for example Alpesh has an Android phone and he uses multiple apps, browser YouTube etc). Whatever he is doing on the phone I want to get all those things from behind (which apps he has installed, which app he opens and what he search on the phone, All these data I want to get programmatically so what all can be get in android).
For now I am aware that installed apps list can be get easily but I want to get usage history and what he do all on mobile.

This is not a code solution, but an answer to your question, so you can get start some where.
In my opinion your question title are asking about two things.
(part 1) Getting User Behavior on the Android Phone (part 2)(App History, Browse
History etc)
1- First part Getting User Behavior on the Android Phone:
There is a concept called context awareness. Short described; it is about gathering different information from the phone, like light sensor, motion sensor, sound, location or even user behavior etc. and depending on your app requirement and the gathered information:
You could send these information over cloud data store for statically usage
You could make your phone doing (behavior) different things depending on location, motion or what ever.
etc.
For context awareness it is an open area for pervasive computing research. And it is not just few lines of code to write, it is typically a complete solution depending on requirement. Example I have built a context awareness application to gather noise collected by phones from different locations for research purpose inspired from this framework, but I am pretty sure you can find other frameworks or even build your own, as I did in my case.
The mentioned framework has some examples.
2- The second part is about App History, Browse History etc.:
This is possible, but you still need to build a peace of software (App) to collect all these information (logs) from the phone. Hereafter you can make phone act on different conditions and/or again send it over a RESTful API over cloud service data store, there is no limit for it.
The problem is, there is no thing out of the box for your requirement. Even if you find frameworks you still need to research it and further work on it.
You can find different examples for your requirement, like to collect browser history, you can find SO question here:
Get browser history and search result in android
Or get list of installed application:
How to get a list of installed android applications and pick one to run
My point here is you need to solve small goals at a time and put your knowledge together at the end.
Both 1 and 2 can also be related to each other, depending on your achievement.
Conclusion
Make a goal to your project.
Define the main requirements and tasks of your project.
Research your options (Technology, Cost, Target Audience, What data I can or I should not collect, what is possible to collect, what is the limits, Privacy issues etc.).
Split your project in small assets and try to solve small problems/goals.
Finally you would be able to put the puzzles together and build your final application

but i want to get usage history and what he do all on mobile
This is not possible and shouldn't ever be possible. Each app is sandboxed by Android so apps cannot inspect what other apps are doing. Think about it, you wouldn't want apps to be able to intercept private information such as banking details.

Every app is isolated from the other ones. Unless you develop a system signed app, you will not be able to gather all that data.
What you could do is to develop your own Android Rom where you then develop your data collection the exact way you want. Then you need to distribute your rom, which is another story...

How to make an app unclosable?

After a user opens my application I don't want them to be able to get out. So when they press the home or back button it doesn't let them exit the app. I know there are ways using a service to keep the app always running in the background, but I don't even want them to even exit.
Is this even possible, if so how? Without having to hack the kernel.
I know this sounds odd, but it is not for a commercial app, but for my lab, it will never be on GooglePlay. The tablets will be given to little kids and they will take a test on it, so I can't have them using youtube or anything else.
Related post: Android, How to make the task of the app unclosable? Only closable by task killing
The answer by CommonWare seems to indicate that kernel hacking is the only way, but is it?
Also I am using Android L.

there is no official support yet - there will be support with android L via the Task locking API
The L Developer Preview introduces a new task locking API that lets
you temporarily restrict users from leaving your app or being
interrupted by notifications. This could be used, for example, if you
are developing an education app to support high stakes assessment
requirements on Android. Once your app activates this mode, users will
not be able to see notifications, access other apps, or return to the
Home screen, until your app exits the mode.
https://developer.android.com/preview/api-overview.html
EDIT: as you said you use L this got obsolete - but I leave it here as a hint for others
said that - you are also able to get this kind of work without root today if you have to ( e.g. kiosk mode app on a certain hardware ). It is not simple - and no solution that works for all devices - but if you need it you can get it work with tricks like:
- reacting on home-screen intent ( and setting it as default )
- when you go to background - bring your self foreground again
- ..

It seems google has some thing called COSU for setting up single-purpose devices
Android 5.0 Lollipop introduced two new ways to configure Android
devices for a single purpose:
With app pinning, the device user can temporarily pin specific apps to the screen.
With lock task mode, a user can’t escape the app and the Home and Recents buttons are hidden. Additionally, lock task mode gives the IT
administrator a more robust way to manage COSU devices, as discussed
below.
and
As an IT administrator, you can configure Android 6.0 Marshmallow and
later devices as corporate-owned, single-use (COSU) devices. These are
Android devices used for a single purpose, such as digital signage,
ticket printing, point of sale, or inventory management. To use
Android devices as COSU devices, you need to develop Android apps that
your customers can manage.
from here
and there is a code lab for it here
for earlier versions of android here i founded How-To Create a Working Kiosk Mode in Android which shows some hacks for disabling buttons and restarting the application after boot and lock. note that most of these hacks, don't work on android 6 and later

Android - Can PushLink do silent updates?

Does anyone know if PushLink can do silent updates? That is, download the app and install it without any interaction from the user?
The PushLink website is quite sparse on documentation regarding features available so I can't be sure.
Or does anyone know if it's possible to have a silent installer for android? I basically have android devices that will not do any user interaction and I need to be able to update my apps running on them.

Yes, it is possible since version 3.1.0 released at 2012.04.23.
Take a look at NINJA strategy
NINJA (Only for rooted devices) The application is just re-launched in
a new version. There isn't notification. BETA!

There's no official way to install anything on Android device without user interaction. Which is a good thing, because it prevents a lot of possible malware and exploits from working.

Android - Setting usage flag

I am currently creating an app and would like to create a demo version (free) and a full version.
However, I am wondering how I can set some sort of flag so that when the demo version has been used 5 times, you have to buy the full version to continue using. This usage will be detected on a submit button.
I was considering setting a flag in the app, however releasied that the user could uninstall the app and then re-install it overcoming my set flag (as this would set it back to 0).
Has anyone got any clever solutions for my little dilema?
Thanks

You might want to try one of the techniques in this answer: https://stackoverflow.com/a/996288/1205715

I think that is not possible with an local application.
File saving to sdcard with strange filename can be a way but It is not perfect.
In my opinion, Right way is using an application server that manages user run times with unique UUID.

It might also be worth thinking about an alternative approach.
In app purchases are now available, so you could have a free and a restricted section in your app, and use the in app purchase to unlock the restricted section. You see more developers going with this approach these days, rather than managing two versions of the app.
Also worth considering the fact that if you have a paid version of the app it can be pirated pretty quickly, one person just needs to get their hands on the full apk. However, if you go with the in app purchase model you will be letting google handle a lot of these issues for you.... just a thought, and the road I will be taking with my next app.