Your friend can NOT claim your child.

There are two types of dependents, "Qualifying Children"(QC) and standard ("Qualifying Relative" in IRS parlance even though they don't have to actually be related). There is no income limit for a QC but there is an age limit, a relationship test and residence test. Only a QC qualifies a taxpayer for the Earned Income Credit and the Child Tax Credit. He definitely cannot claim the child as a QC, because, as you stated, he is not related. 

A qualifying relative dependent only gets the taxpayer the (up to)  $500 other dependent credit.  But, your friend doesn't qualify for that either; see rule 6.

 Qualifying relative dependent rules: 

1. Closely Related OR live with the taxpayer ALL year .
2. His/her gross taxable income for the year must be less than $4200 
3. The taxpayer must have provided more than 1/2 his support
4. He must be a US citizen or resident of the US, Canada or Mexico
5. He must not file a joint return with his spouse or be claiming a dependent of his own
6. He must not be the qualifying child of another taxpayer

In addition to the above requirements, to claim your friend's children, they must meet all of the above requirements and:
--- your friend (you in this case) must not be required to file a return,
--- he/she does not file a return claiming the children

You can claim your son on your own tax return since you worked and may be able to get child-relatd credits and file as Head of Household.  But something else seems fishy--how is a "friend" getting Medicaid for your child?   Is this "friend" the child's other parent or a relative?