Μια μπύρα [παρακαλώ] /mja ˈbira [parakaˈlo]/
“One beer [please]”
The “please” is really optional. In fact Greeks tend to get creeped out by such politeness. But as a foreigner you’d probably be expected to produce it.
DaH HIq HInob /ɖɑx xɪq xɪˈnob/
“Give me alcohol NOW”.
Any similarity of the word for alcohol and “hic!” is purely intentional.