I am IMG, I have a valid Emloyment autherization document (EAD) ,but at the same time I have a case in the court (ASYLUM case) and its pending and I am now I am in removal proceedings, so can I work with my EAD in residency program if I get matched, or does removal proceedings will affect me?can I apply for program and work with my EAD even if I am in removal proceedings for pending Asylum case?
This question is very important to me.

I would most definitely speak with an immigration lawyer. Technically, you can work on an EAD. Once you are in removal proceedings, doesn't it move fairly quickly? I'm sure that you'll find out whether you can stay before the match actually happens.

I'm sure that at interview, the program will ask you as to why you have an EAD and when you're gonna get your green card. I can't imagine they'd take a risk on matching you knowing that you may get deported.