I have a question: if I buy a version from itch.io and there's an update, will I have to buy the new version again, or will it update automatically? It's my first time buying from itch.io, and I'm not really sure.

No, once you buy it all updates are free (does not include DLC on games that have any) and show up in your library, itch.io app, and a bar at the top of the game page as seen in image provided. Usually when purchasing games on itch they will show up as itch.io on your bank statement, though for me at least this one showed up as "End of Time (something)". I had no issues during or after the purchase so it should be the same for you. Worst that may happen is your bank calls to let you know an international charge was made to your account and you have to verify that yes you bought stuff.