When a speaker refuses to make eye contact, it may indicate that they are uncomfortable, insecure, or trying to avoid a connection with the listener. It can also suggest dishonesty or lack of confidence in what they are saying.
I am assuming you mean to say, "What do you call someone who refuses military service on the basis of religion?" A Conscientious Objector
A mustang is a wild horse - when you use this slang to mean a person, it is a person who refuses to settle down and be tamed.
Yes, it can be considered theft if someone refuses to return your property, as they are unlawfully keeping something that belongs to you.
to watch out for them
It means you look too overdressed and retro.
Nonjuror
No, it doesn't mean he's gay. Maybe he's tired of answering questions about it. Sometimes people who "look gay" are not gay at all. You can't really tell by looking at someone if they're gay or not.
they look at you through the corner of their eye or take a quick look
Peer
They look like both genders
boycotter