it appears given he is held on a no bond extradition warrant much of your answers are obvious. From that alone I would say yes, they will come get him. Whether he wants to go back to Kentucky doesn't matter at this point.
Of course he can try to fight extradition. Chances are he won't win the battle but there is always a chance.
If he doesn't fight it or loses the fight, as long as Kentucky is willing, he's going back to Kentucky. What happens there is going to depend on how much he owes and what the judge does as the judge has many options in such cases.
the only help you can be is a source of lots of money to either pay for an attorney or pay whatever child support the court demands before releasing him.
Now, of course this is not taking into consideration failure to pay child support can become a criminal matter after a point. If it is a criminal matter, he will want an attorney to represent him. Again, your help would be limited to throwing money at the situation.