This app was mentioned in 10 comments, with an average of 1.60 upvotes
This is the free version of the app I've been using for quite some years now. I can't speak for how intrusive the ads are because the paid version doesn't have them.
It supports full cell highlighting like you're asking, puzzle analysis, hinting, generation, colouring and reasonably defined difficulty levels. My only complaint is that entering in an existing puzzle from another source (like /r/sudoku) is so convoluted that I'd rather go to my computer for it.
If you like solving Sudoku, Sudoku 10'000 Free is my favorite game. Awesome gameplay, hints, etc. Catch it here.
And I also like Temple Run for its smooth and fun gameplay.
This app is really customizable
Sudoku 10000 is one of the better apps that I've used recently, although it's very infrequently update. But even still, it's very feature rich and has a large collection and both easy and very hard puzzles
I suggest you get an app that can analyze your puzzle and tell you what strats are required to solve without telling you exactly where. Work your way from a low difficulty, only moving to the next once you've mastered the strats the generator uses in that one.
For reading up on specific strategies, the following resources are invaluable:
Start with intersections and naked pairs. Naked triples should follow and then learn X-Wings. Don't try to learn more than one technique at a time.
Enjoy the game and come back to us if you need any specific help
I play with Sudoku 10,000 but I was talking about one I wrote myself.
There are many ways to learn about Sudoku techniques.
Games (to get you started)
Sudoku 10000 - https://play.google.com/store/apps/details?id=com.onegravity.sudoku.sudoku10kfree
Microsoft Solitaire Collection - https://play.google.com/store/apps/details?id=com.microsoft.microsoftsolitairecollection
LiChess - https://play.google.com/store/apps/details?id=org.lichess.mobileapp
1945 Air Force - https://play.google.com/store/apps/details?id=com.os.airforce