Translation:Da, te rog!
Saying (te) rog is more informal, you say it to your friends, family members etc... On the other hand, (vă) rog is meant to show respect to a person, like your boss, your teacher, an important client.... It's called a pronoun of politeness. Vă is in accusative case. In nominative case it is dumneavoastră. Hope you know what cases are ;)
that kind of misses this question, frate... So "te rog" is used by a single person when it's adressed to someone of the same age/status... whereas "vă rog" is used by still a single person but adressed to someone that is older/more respectable than you (like a priest)
You are correct. This is precisely what I explained in the comment :)