You list ALL addresses. Better be safe than sorry. I would absolutely not do it on your own these days, get an attorney to do it correctly. This...

How do I know if I currently have an ongoing case?

Start with checking mycase.in.gov - that is public information

That doesn't mean a whole lot, unfortunately. It just simply means they reviewed your fingerprints, literally, without conclusions, promises,...

What should I do?

You need to sit down with immigration attorney for a full consultation as soon as possible.

How can I get a copy proving my x wife was already married in Cuba when she married me

I believe US has a section in Embassy of Switzerland in Havana. Call them and see if they can help you with obtaining records

How do i file for emergency custody?

Get an attorney to properly draft a motion and prepare for the hearing.

What can give a father full custody

The Court will have to decide what's in the best interests of child. Google: Indiana Code Title 31. Family Law and Juvenile Law §...

Custodial parent died, do I get automatic custody of my child? Can grandparents refuse to give my daughter to me?

There is nothing automatic, you need to request that and provide proof that it's in the best child's interest. Get an attorney ASAP.

How do I sign a waiver of final hearing?

It's hard to exactly where you have to sign without seeing the forms. Are you using an attorney? Is the other party using one?

Will my ex avoid paying child support by claiming he is too sick to work?

Not necessarily. You need a good attorney to rebut his arguments and advance your position.