Can a fossil be reborn?

Excellent question! There's no definitive way of saying "this is a fossil"; so paleontologists usually pick the arbitary age of 10,000 years - so if remains are more than 10,000 years old, they are...

Any fossil can be a frozen fossil, a frozen fossil isn't a type of fossil. It's just a natural occurance to a fossil.

in rivet ravine

Because they are made of fosils

Yes! You can send fossils from fossil fighters to fossil fighters champions via the fossil cannon, located in Ribular town in Fossil Fighters Champions.