Domestic voilence and divorce :India please help!!!

I am in abusive relationship in US and I am on H4 visa,from India.I have a 2.11 yrs daughter and thinking of divorce .I got marriaged in India under Hindu marriage act in year 2005.And I am in US just after that.My daughter is US citizen.

I have few question if you can help me find info or answer them for me.

Can I apply for divorce here?
as per my understanding I cannot get custody of my children as I will have to leave country immediately as I am on dependent visa.I do not have money here for good attroney.

Also is there any way i can be in these country independently,can I apply for green card on my own as an battered spouse..Without my husband knowing about it .How long does it take.
I do have qualifiications required to work and take care of myself and my daughter.

what is my best option?
Also I feel very scared about leaving If can secertly go to my country without telling husband will that affect my case?