1. There are several legal aid organizations that represent / provide free legal help to indigent people (people who cannot pay legal fees; usually require income to be lower than 125% Poverty Guideline). However, the types of service varies. It depends on the type of case you need help with and your residence. I can name a few for NY and MA that provide services for immigration, housing, employment, consumer protection, disability, racial or sexual discrimination.
2. There are several organizations that file lawsuits for social issues (racial discrimination, sexual discrimination..... the list goes on). However, the claim has to be meritorious .
3. This is your question "
Can foreigner file a case inregard of their visa status in US law court?" your query is unclear. If you are asking to bring a claim because of unfair or unequal treatment based on national origin then you might have a case. However, it is a hard case to prove. It depends on the evidence you have. Furthermore, the courts are notorious in not wanting or willing to hear such cases because often time these cases lack legal basis or is not meritorious .
4. If a person is from "x" state and wants to sue a person or entity in "y" state then the case is heard in federal court because this is typical law school scenario when federal court have subject matter jurisdiction based on diversity of state.
I hope this helps.
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