- In the Android Phone-Samsung there is an option in settings called
Full-screen apps - On click of it we have options
AutoandFull screen
Questions
- Is there a way we can programmatically check this from the app
- How to navigate the user for this page for particular app selections from an app with the click of a button

Answer for question 1:
I think you can use this flag WindowManager.LayoutParams.FLAG_FULLSCREEN like this:
Answer for question 2:
Note - both package names here are for example find the ones you need first and replace.
N.B: - be aware that both package names can change over time so keep them up to date or make a dynamic package name search.