This was such a good question, and I wondered as well. Since nobody answered, I googled and found this link: https://hinative.com/en-US/questions/733177. It sounds like "provare" means "try" like test a thing out--trying on clothes or tasting food to see if you like it. But "tentare" seems more like "effort"--like "we tried to get to the top of the hill." I would love if someone who actually knows would confirm, but that's the sense I get from this link.
Yes. For that you need andarsene, literally 'go oneself from it'; Duo would have said tu hai tentato di andartene.
The verb translates to go away, leave, get lost, buzz off and many other colourful ways to say so, short of the full "f... ..f" which has its own Italian slang. Vattene! is an essential word for tourists. I'm not sure I'd remember the plural andatevene! correctly, but it sounds good if you spit out each syllable. :-)
Indeed, in the context of hai tentato di ..., I think you have a good point about the underlying meaning and andarsene should be the verb of choice. However, with a double pronoun (aka two "clitics") they must think it too complex for early topics.