/dia/ is the imperative mode, the mode for giving orders;
da' as a third person is indicative mode, that is the mode for describing reality, and
not hypothesis or wishes;
Answer (all correct forms)
a) mi dia delle birre, per favore
b) mi da' delle birre ?
c) vorrei {una birra, delle birre} [per favore]
I don't drink beer (as it has alcool), but I would use (c).
Another you will hear is:
d) volevo una birra ...
here a fake past tense is used to mitigate the meaning of a direct order
to the bartender; it's commonplace.
About imperative: if you walk around with a friend, and see something interesting, you just say: /guarda la'/ (look there) or /guarda un po' la'/, in the imperative
mode; it is perfectly fine as you are making an order in behalf of your friend.
Imperative mode is the mostly used among friends and between Captain and Soldier.