First i want to say sorry for my english. I'm hungarian and i might made some mistakes :P

So my question is, what if i only have, lets say one hour left but i can't finish my game in that time?
Am i allowed to still publish my game (unless it's literally unplayable)?
And if so, then should i publish it?

Of course if i am allowed, and i didn't finish my game in time, then i would tell people (inside the game) that i run out of time and so the game is not yet completed, but still playable.

You can still publish it. It's better to submit something unfinished than nothing at all! You can always say on the game page that you ran out of time if you do. 

I didn't finish. Should I submit?
Yes! Game jams are about creating prototypes. A finished game takes years. You can still win with a cool idea, even if the experience is brief.