How to run app in background with other apps

I am an Android beginner (but experienced Java programmer) and I would like to know if it is possible on Android to write an app that can do something similar to what a "normal" windowed program in the following respects:

1) Place an application access button with very simple features "always on top", that allows the user to open the application, or paste data from other running applications that has been copied to the clipboard into my app and other simple functions. The button could be a simple circle that is always on top, and certain gestures on the button invoke certain commands in my app.

2) When other apps are running (e.g a browser or a PDF viewer), allow the user to "drag and drop" information (e.g. copied text, URLs from a browser, text copied from a PDF being viewed) into my app which is sleeping (since the other app is currently running). I'm guessing that if my app is "always on top", focusing on its "access button" will make it active?

I know all this can be done in Java Swing, but with Android I anticipate problems. My app will be running in its own protected space (as will all the other apps), so when another app is running, like the browser, I am not clear on how my app can access data from other apps. Would this be a case of requesting permissions to access the data of all the standard apps I would like to access in my app (e.g. browser, PDF viewer, word, excel viewers etc)?

Many thanks for your help,

-Blue