As an illegal account in the United States, can I send money to my family? If I go to the bank, will they find out that I am a black household?

You can't send money home. The credit construction system in the United States is very sound, and they attach great importance to credibility. Once you become a black household, it is equivalent to carrying a stain that you can't get rid of for a lifetime, and what you do (dealing with money) will be limited. And the bank will definitely find out that you are a black account at the first time.