When should I give her space?

Try to comfort her- if you care about her wouldn't you want her to know? but if she wants space you should give her space do something that you both agree on doing...

My opinion. Talk to her and ask do you need some space? And move on from there.

That's vague, depends on the problem. the perfect way to deal with a mild - moderate spat (in my opinion) would be to stick around. some guys will leave the house because they can't stand tension or are upset, I think it shows maturity and a certain amount of commitment to just stick around, read or something private and wait for a good time to have a conversation. but I'm not really sure what you mean by 'problem in the relationship.'