Lighter Stockfish Engine

When i analyze my games in order to see the best movements I should have made. I feel how my phone heats up and battery drains faster. I think this is normal, but as long as I don't need too much power to analyze my game I wonder if I could use a worse stockfish version because I don't need a deep analysis.

You actually can! When you are in analyzis mode there are several buttons at the very bottom, the gear gives settings for stockfish where you can change (among other things) how much of your phone's memory it uses.