You would say: Things are in place now. I need to keep my room tidy.

It's not clear what you are trying to say. Are you saying that the room is clean and you plan to keep it that way in the future? Are you saying that you just cleaned your room and you want to express that you shouldn't have let it get messy? What do you mean by "need to"? Why do you need to keep your room tidy? I've put everything away and I'm not going to let my room get messy.

I think what you wrote is ok, although it is very informal. However, the saying is "Everything is in place." Not the place.

Only one thing. Everything is singular so it should be Everything is in its proper place now.

I understand what you are trying to say, but the first part is not entirely correct. I would try something like this: Everything is in their proper place now.