The child's father can certainly challenge you for custody if your BF is living there.

You can ask, they can decide whether to answer................................

This simple Q&A forum is not a substitute for what you need, which is a full review of all the facts by an attorney.

If he isn't working, he won't be paying alimony.

This is a Q&A forum. You have not asked a question.

Of course they can.............................................

Can you sue E-bay? Yes. Will you win? I doubt it seriously based on these facts.

One thing they can use is your confession on the Internet. You are suspected of a crime. Shut up and lawyer up.

When one asks "Can I sue" the answer is usually yes. But suing a mega corporation over these facts is a pure loser IMO.

You have a lawyer. That is who you need to ask.