1) Can he find out he is moving at 0,5c in relation to someone?
Of course he can find out he is moving 0.5c in relation to someone. When you are in your car, do you have any difficulty determining that you're moving at 50mph in relation to a nearby pedestrian? This is in priniciple no harder at .5c than it is at 50mph.
2) What gurantee our whole universe isnt moving at 0,5c in relation to another far away observer?
The guarantee is that there is no such faraway observer. If he's an observer, he's part of our universe.
3a) Will he assume/is he right to say he is at 0c0c?
I can't figure out who "he" is, but any non-accelerating observer is moving at 0c relative to himself, and is entitled to say so.
3b) Can particles that dont interact to the universe, in their perpective, say they're at rest?
All particles interact with the universe, because they are part of the universe.
Final unnumbered question: I can never be guranteed or assume myself to be at 0c/rest, since there's a possibility someone far away can see me at 0,5c?
You are at 0c relative to yourself and .5c relative to someone else. There's no contradiction here. All speeds are relative, and it makes no sense to ask what your speed is until you specify relative to what. Different specifications will then give different answers.