Settling custody cases is done about 95% of the time, meaning only about 5-10% of cases go to court. It's not necessarily indicative of either...

You can't stop him from filing anything; you just have to deal with it.

You have no power or rights in this situation at this time.

You need to hire an attorney to straighten out this mess.

It's called manipulation. Don't accept what he brings.

You can use your phone or facetime and mediate separately (not in the the same room).

That is not possible to answer without knowing why your home is not fit. Get a consultation with a local attorney to discuss your response and how...

You don't have to give the child the father's name or list him on BC. Make him prove paternity himself.

An attorney has the same methods of service available to them as any agency. Call CS and tell them to serve him personally at work.

If the subject of the power is still competent, get a new POA the correct way.