Does it affect my husbands immigration status if our child and I apply for or receive Food Stamp Benefits and Medicaid?

Hi, receipt of public benefits does not automatically impair one's immigration status. It appears that you need to provide more information re. your situation and what your plans are.

Assuming you are a USC, no, but that means you might not have sufficient income to file I864 and need to utilize a joint sponsor.

There really isn't enough information to answer this properly. U.S. citizens can generally gain public benefits without triggering any public charge problems for their noncitizen family members. However, if you are trying to petition for him to gain legal permanent residency then it sounds like you won't be able to sponsor him. See an immigration attorney and speak to the attorney about a co-sponsor.