Can I submit I-485 without vwp stamp

Not a huge problem if it's the way you describe it. You have to prove you were lawfully admitted, but the combination of the faint stamp and...

I am waiting for my residence abroad Mexico, my fiance and sister are taking car of my daugher on USA, could CPS take my daugher

This isn't really an immigration or green card question. Who is your daughter's legal guardian? I suspect that could be the issue. There also have...

You should be OK as long as you have the travel document

Can I apply for an Immigrant Visa as a Spouse or Fiancé of a U.S. Citizen while I am on a J-1 trainee visa?

This shouldn't be a problem (assuming, of course, the marriage is a genuine one, which I'm sure is the case)

Do i need to present my divorce paper from my home country before getting married to a USC

You'll need it for immigration. Try to get it. If it's really not possible, you can go with affidavits and other secondary evidence, but this is...

Can I get my permanent residence ?

This sounds ok. But in cases like this, it is best to work with a lawyer who handles these regularly.

Transferring to another school - F1 Status

Yes

Priority date current in Sept, can spouse on J1 with 2yr home residency condition eligible to apply for AOS along with me?

She'll need a waiver.

Can he stay in the U.S. due to the inconsistency in the paperwork? Is there any possibility of bail or release with bracelet?

Mr. Murphy is correct. The deportation order could be reinstated. That's the biggest hurdle here.

Can I apply citizenship now or later?

You should work with an attorney on things like this unless you have a squeaky-clean case. You're probably OK, but it depends on timing and a...