As I know Almost have the same meaning but: 1. هست is easier to use and is used more because of easy tongue. 2. هست has two meanings: firstly, "Be" and another one "Exist" but است just means "Be".

both of them have same meaning but "ast" is more formal than "hast" good luck!

same meaning. however است is more formal

They surely are infinitives, just not commonly used as such.

yeah, ok. I meant "است" and "هست" where did that "ن" came from ?!! lol sorry, my bad