That child will probably go down in history

His father's name will be Phillip Fry

The Chosen One

Nope! Just as Britain doesn't have to say country on stamps, you will only need to show your PoB (Planet of Birth) if it is not Earth as it will be assumed that is the norm. British stamps don't have to put their country name on them because they were the first place to use them. It's called naming rights and is fascinating.

Will this kid rebel against Earth or stay a colony

No we won't, at least not with the first person born on Mars. Currently, any and all trips to Mars with humans, are no return trips. It will be a while before it gets to the point where planetary travel will be fast enough for a return trip to be worth doing. *continues to shit on your dreams*

If they are, not when (unfortunately).