Malignon is correct.

Standard down payment is 20%
Unless you get a home that has FHA which sometimes can be as low as 3%.

Other than hearing from people here.....I have not heard of any bank ask for immigration information for a loan or mortgage. I work for a bank that is unethical practice and discrimination.

Documents needed are simple: recent 2 years tax returns, SSN, income information, credit score.

Make sure you don't have high debt and your credit is good.