Can I get a restraining order on someone if we live together and the house is in their name?

Yes you can. It doesn't matter if you live together or if the house is in their name.

If I die, will my daughter be able to stay with my partner and not go back to her biological father ?

Its unclear if your partner has any standing in custody of the child, although new case law is changing that.

Lost the Traverse hearing for failure to show cause in a divorce default judgement

I think you have asked this questions numerous times. The Order will stand. You need to speak to an attorney to see what relief you may have.

What evidence to bring, and what to expect?

I strongly suggest that you speak with an attorney. Unless he is a "bad guy" the court will grant him some sort of visitation.

There are complicated matters that can take a while to adjudicate. You are much better off working out a deal with him to allow it, than let it...

I never put a child support order in cause I could not find his father. I found him 33 years later can I file for support . ?

If your children are over 21 then its too late.

How do i file for a poor man divorce ?

You need to go to the pro-se office with your benefits card.

Does New York State law require me to evict my boyfriend from my home?

Since he has lived there more than 30 days you need a court order to evict.

What happens if I lose an order to show cause in a divorce case does the Judgment for divorce get automatically filed

You've asked this a few times. You need to speak to an attorney.

When a Divorce case is dismissed with prejudice and did not go to trial, can I still file suit again against the same Defendant?

No. You cannot prevent someone from divorcing you if there is proper jurisdiction. A court cannot order you to stay married.