Approach it directly. Like everything else. Next time he says he’s sleeping over, say hey since we are doing XYZ when you sleep over, for both of our safety id like to discuss if we have other partners.

As about other stuff , how is he paying child support? One can’t be without stable full time job if they have to pay child support. Is he not paying in full? Accumulating arrears? Id not ask that directly, perhaps it’s intrusive, but you could ask how often he sees his child? That’s legit question.

Simply making ends meet when you are on your own and have no obligations, maybe, free-styling and maybe not needing much could be ok. Not with 11 year old!