(2) When someone's husband dies, we say widow. I wonder what do we say If someone's husband not died but he went off with some other girl; or if someone's husband was so arrogant that he told his wife to go back his home and no more he doesn't want her and he is going to marry other girl. How do we say such a woman/lady/girl?

She is a deserted wife

A grass widow is a woman whose husband is away often or for a prolonged period - as an extension, if the husband goes off to play golf every day, she is a golf widow.