What would be the best thing to do?

File for custody, and retain counsel please.

.....?

As counsel said, you really need to obtain counsel to help you and protect you.

Is it mandatory to register order once I move?

Unless you need judicial intervention you do not need to register anything.

Unless the parent is disqualified the parent will almost always trump the non biological relative.

Uncontested means that everyone agrees on ALL issues. If one side doesn't consent, then they can proceed by filing an Answer and proceeding...

It will be really hard unless you can produce the real father.

What if the judge put a order of protection that i did not want there and i still kept in contact with the person?

You run the risk of arrest for violating the Court Order.

Can I ask for a counter order of protection - without going to trial?

You would need to file for your own order of protection, and hope they give you the same date and judge.

Child support if I have more time ?

You can, I would strongly suggest it. Please speak to your attorney.

Power of attorney ?

You really should speak to your attorney for advice.