Child Custody and Alimony

Hi, I am a PhD student in USA (F-1 Visa) and I have a 4 year old kid, who is on F-2 Visa with me. I am getting decent stipend while doing my PhD. My husband works in another state (USA) and earns good money. We both have differences and he often threatens me with going back India, so I will be in trouble and I will end up giving custody of my child to him, because he is financially strong, that's what he thinks. Technically I earn decent money and can support both my kid and myself while I am doing PhD here. I want to know how true is his understanding that as he is financially stronger, he can anytime withdraw his support for me and can have child custody. My kid is very much attached to me and I find him alluring my kid a lot these days. I am afraid in case he decides to go back India, can I still have my kid with me, just in case if I need financial help, would I be able to claim help from him while he will be earning in INR and I might need dollars? Does that make sense? I even afraid of his decision to leave off the job, so he can tell to the court that he is not ultimately he is against my decision for PhD in US as he knows I will come out as stronger person after completing it. Please guide me over this....also what if I someday give up with his abuses and decide to take a divorce, can I still have child custody, if I am not financially strong ?? In that case would I get alimony ? and is separation period still required to get a divorce?