If I have been a legal permanent resident for a year and have a family sponsor, can I ask for food stamps and disability or can I either myself or sponsor at risk?

Yes, you would be at risk. You cannot obtain specific cash received benefits. In addition, if you obtained it through a family petition, you had an I-864 signed on your behalf, then you may be required to pay the gov't back.

No, you cannot ask for means-tested public assistance because the government will go after your sponsor for reimbursement of any funds the government provides to you.  That is the concept of the sponsorship for the affidavit of support.  If you do apply, you need to put the sponsor on notice that this is the case.