1. Yes, sort of - issued desert gear a long time ago
2. Never
3. No - see #2
4. No, but you must look, er, unusual with a baseball cap on top!
I've used a long woolen scarf as a head/neck/face wrap in extreme cold when I didn't have anything better to use.
If you like it, use it. I never really used mine for various reasons, half of which I've forgotten.
Tom