Yes some are forced to comply with the muslim standard.
Well if we could be honest with ourselves and remember how the original women of god dressed I believe they wore the head scarf ... Let's let's not dress for the times ( our-self) but dress to please god
Yes a lot of arab christians wear head scarf hijab. And also in rome and italy ,and catholic nuns also wear head scarf. It shows mark of respect before God to cover urself and have dignity and comitment to worship of God. Also some jewish woman cover their heads, or even shave their headsand wear a wig to cover their hair? So I think many religions do so!
If I am reading your question correctly that this is about a arab woman whom is christian not muslim: That being the case it is not required at all in christianity. She may feel better with one on but this is her choice not a law.
No ,and no body would force her to wear the head scarf ,but if she did its her choice.