Note: i don't want to delete my account but i have some question related to it.

As far as i know anyone anytime can delete their itch.io account once done the account and it's content is no longer accessible.

what i want to know is:

1-if i purchase a game and the author/owner of the game want to delete his account what happen to the game? will it be removed from my library?(regardless if it was paid or free).

2-are there any extra step that i don't know about?

If you bought a game, the creator will have to contact support and give a good reason to delete their game in the first place. As long as they have games owned by someone, they can't just press a button and delete their account. If their request is approved, then yes, the game will be removed from your library. That's why it's not so easy to do.