Not even DL's Portuguese lessons taught me. I'm guessing in Latin context, "vă rog" means something like "I ask you, please". Correct?
yes, you can translate it like that, also :) but in this context, "da, vă rog" is translated as "yes, please": Vreţi lapte la cafea? Da, vă rog. Do you want milk on coffee? Yes, please. the verb is "a ruga" (to ask) can be used in many ways: Te rog, dă-mi sarea. - Please, give me the salt. Maria l-a rugat pe Mihai să o ajute. Maria asked Mihai to help her. Eu mă rog în fiecare zi. I pray every everyday.
'Vă rog' is for the 2 person plural, or it can be also the singular but for the polite form. Te rog is just the 2 person singular.