Develop Reference

What Box like view should I use?

I'm trying to create an app using Android Studio, and I want to use some type of expandable box, where I'll have an indefinite number shown like in a stack, and when clicking on the left side icon, the selected box opens up to show more info.
The basic idea of what I'm searching for:
Would anyone know about something like that??
Thanks in advance.

If I understand it well, what you're looking for is a recyclerview (for the indefinite number of row) and an accordion widget to open close your content.
I will suggest your to look at these projects:
https://github.com/hgDendi/ExpandableRecyclerView
https://android.jlelse.eu/get-expandable-recyclerview-in-a-simple-way-8946046b4573
which present all requirements you need.
And here is an similar question/answer : https://stackoverflow.com/a/10313432/6809926
The google search I made : android accordion recyclerview example.

Equivalent of Android radio buttons with no popup and one selectable choice?

I want to create something similar to a listpreference menu item with a single selectable option out of four options. The problem is that descriptions are necessary for each selectable option and they are rather long. Shortening descriptions further isn't an option.
The Android app I'm working on currently uses a custom method for displaying a menu item's summary field. The summary calls an int which points to a string reference stored in a different file that displays a string. I tried using %s as the summary to update the summary with my selected option but that literally returned "%s". I don't think the current method supports dynamically loading summaries.
My next idea is to create a submenu with four selectable choices (maybe checkboxes?) and only allow one to be chosen. I think this is essentially a listpreference menu item but allows more space for separated descriptions. Is there a preferred way to accomplish this? I'm trying to avoid re-writing the original custom method for displaying descriptions as it works well for the rest of the app's menu needs.
EDIT 1: An image will help explain what I want. See Android sample settings menu. I want to create a section similar to the "embedded frame buffer" section in a submenu except only one of the three options are selectable. This approach will allow me to have more room for separated, long descriptions. Perhaps I'm looking for radio buttons with no popup and one selectable choice? Is this a thing in Java?

Not sure if I understand the question correctly but instead of a list of checkboxes where only one checkbox is checkable use a RadioGroup with Radiobuttons. You can have multiple RadioButtons which you add to a RadioGroup and then only one RadioButton can be selected.

Sliding down and up ListView with additional data (innitialy hidden then after click showing up )

I want to create some kind of ListView which will be expanding and collapsing after click on one of its item. When item of ListView is expanded show additional data. After I click another one first data collapsing and show actual one. I found one solution (https://github.com/SilenceDut/ExpandableLayout) but I'm thinking that should be other ways to do that without using external library. Am I right ?
P.S sorry for weak english

You can do it using Expandable List View:
Tutorial Link :-http://www.androidhive.info/2013/07/android-expandable-list-view-tutorial/

Show an option list after click on EditText

I've one seen on an application for iPhone an interesting idea which consists of showing a list of options when we click on an area for text edition. For example, imagine I have a field called "City" (EditText) which I am suposed to enter the name of the city. When clicking on the EditText, a list automatically shows up with a few city suggestions (e.g. defined by the programmer) which can be selected. If the user doesn't like the suggestions, he writes the city himself and this city can be saved for this list for future.
I want to programme this on my App for android. I need that, when clicking on the EditText for introducing the data, a list automatically shows up with some suggestions defined by me (Programmer). However, I don't know how this can be done. I've googled but maybe it's hard to find the correct keywords to find a similar topic.
The idea is that the user should use the names already written in the list in 90% of the time and just write himself the new ones when it's necessary. Something like a dropdown list but with possibility of writing new stuff instantly without specific option.
How can this be achieved?

You Need Something Like View in android Named as
AutoTextComplete
Examples How to use this :
help
Best of luck

You can consider focus changed listener for Edittext,
when focus is gained you can show a context menu to choose data from.

GWT- PopupPanel with search?

I am looking for a way to create a popup dialog box when a user double clicks a textinput field that will contain a scroll-able list (from database table) where the user can select a field, hit ok, and have it placed into the textbox when popup closes.
The other major requirement is to have a filter/ or search field in the popup to aid the user in finding the correct option to select from quicker.
What is the best way to implement this?
Modification to gwt's popup panel? maybe a JOptionPane? are there any simple solutions already designed for free commercial use?

You could implement this with a com.google.gwt.user.client.ui.PopupPanel. You can make a PopupPanel that contains a ListBox with your data from the database, along with a OK button. When a user selects a value and hits OK, you should utilize an EventBus along with a custom Event that will pass the value to the field on the page. The page will have an event handler that will catch the event and put it into the field.
Another option is to use a com.google.gwt.user.client.ui.SuggestBox. It is a box that autocompletes / suggests values as you type, kind of like the Youtube search bar.
I can offer more resources to help you accomplish this, if you'd like.