Can this mean a date, as in what day it is, or a date, as in going out to eat with a boy/girlfriend?
only what day it is.
In the text-to-speech, it kind of sounds like the accent is on the second syllable. Is that correct?
I am bad with recognizing where the accent is. Anyway, in Polish the accent is almost always at the second-to-last syllable. If you hear it somewhere else, it's for 95% the case of an imperfect audio.