Hello, Itch.io manage the accounts and purchases, so yeah, when you buy the game, it adds it to your library, so when you want to download an update, just log in, go to your library, and download the game :)
As for the performance issue, thank you for the feedback, we already made a lot of optimizations since the first release, but we continue to do so. We'll check what can be happening for this performance drop after 20 mins of playtime.