Actually I use the plane screen app when available to save the battery. But when not - "Chess Free" on Android. I am not a great player so I have no idea if the AI is good. It beats me pretty often :)
Lichess, hands down.
Definitely lichess
For those who like it hardcore, freechess.org is where it's at. They do it for the game, not for the money.
If you're not playing on Lichess, you're on the wrong site. I am USCF 2100 and have played on almost every chess server. Nothing comes close.
Nice rating man, good job. I know how hard that is.
For playing I like tChess (on iOS). It costs money but was worth it for me.