The assistant professor doesn't answer e-mails I'v already read the similar questions here, but i'm sure those are not applicable in my case. 

The assistant reminded us during the last session that we can contact him via email, he is only responsible for a chapter not the whole course. Usually my professor teaches the theory and his assistants handle the exercise sessions.

I tried to contact the person twice via email about fifteen and five days ago respectively, but I have not received any response yet, and I'm not expecting any response at all based on his behaviour before.  

I really need an answer before the deadline, so I decided to to contact the professor himself, explaining why and pose my question to him, but after consulting with some academic people this is going to be highly irregular. I don't really know how to handle this in an academically manner.
15 days ago was the weekend before Christmas, 5 days ago was new years day. I am not surprised the assistant hasn't answered: my university is closed till Monday. Since I have children and the school and kindergarten are also closed till Monday, I have very little time for answering emails. Moreover, this is the time of year to focus on other things than work (why am I writing this answer?).