Call the cops. The state may require him to pay restitution. Hopefully, he is now your ex.

Your question doesn't fit the narrative you posted. Teach your daughter not to fight. Report the assault if you want to. None of us can advise on...

Imagine being in Mexico and the warrant shows up. You risk going to a Mexican jail awaiting extradition. Any of this sound like a good idea?

You have asked the same question at least three times. The answer isn't changing.

We don't know the laws of Costa Rica or Nicaragua.

Yes, they can sue you. A judge will decide who is telling the truth.

Unless you can prove those statements are defamatory (and it doesn't sound like they are) there is nothing you can do.

You will need an engineer to testify that the product is defective and that is what caused your counter to stain.

No, you cannot sue the judge....................

I don't think any custody court will care...........