1. I they lodge an false FIR Against me and my family members, them what is the remedy?? Can we apply for anticipatory bail or other.
You first have to obtain aB and then challenge their false cases in the court of law.
2. I dont want to live with her, what is the solution??? What may be the compensation
Forget about the compensation, first file a divorce case which will bring lots of solution.
3. Whether all of these may create problems for my family members who have no connection with her .
Yes, certainly it may bring disgust among the family members due to her false activities.
4. Whether i may take any legal action against her and her younger brother whose call recordings i have to abusing me , my sister very very badly, and threating me to murder.
Call recordings may not entitle yo to file any case against them, but you can very well lodge a police complaint for their threatening activities including extortion.