Is there a way to keep the top menu (category, Latest, New, Unread etc), displaying when going into a topic?
No, there is not. Visually I am not sure how you would get that to work.
Yes, I think that stacking navigation headers that, as long as the logo and hamburger are present, are at most only a click away, could make for some cramped screen real estate. Especially for mobile view.
Got a mock-up of how you think this could look?