Yep, tu is informal and voi is formal. A lot of languages in Europe have this. The French tu & vous, the Dutch jij & u. I'm dutch, if I would ask a teacher something I would say "u" and not "jij". In English "could I" is also more formal than "can I", right? It's like that.
Pimsleur teaches that 'stare' literally means 'to stay' but that it's used as 'to be' when describing conditions, feelings that change frequently, like 'i am well'. They use examples like "Lei come sta?" (How do you stay, meant as How are you?) "Io sto bene." (I stay well, meant as I am well.) They say you use 'essere' when describing characteristics, things that dont change or dont change often, like 'I am Italian.' Examples were like "Io sono Italiana."
That's what Pimsleur taught, anyhow.
Just to be sure: is the difference between "stare" and "essere" the same as "estar" and "ser" in Portuguese? I mean, I've already seen here a sentence like "Dove sei?" and I got somewhat confused, Idk I'd think "Dove stai?" would be better (provided that these two verbs works like "ser" and "estar" do in Portuguese).
I was expecting this to be the case (I speak some Portuguese from having lived in Brazil), but it seems it's not the same unfortunately. Italian uses stare a lot less than Portuguese uses estar. In many cases where Portuguese would use estar, the equivalent Italian sentence uses essere. I think this is also confusing for speakers of Spanish, which is more in line with Portuguese in terms of the use of these verbs.
I too, had learnt the actual definition of this as How do you feel. Hovering over the words in Italian backs this up. Is it not just used as a generic greeting expressing an interest in how the person is, yet the translation does indeed mean how do you feel?. I think it is important that Duolingo clarifies the true meaning, but the usage too. In English I might ask How is it going. I don't really mean How is IT going, but more colloquially I am asking How you are, so surely the message and the translation should both be correct. In this instance I was marked wrong for How do you feel.