If the non-custodial parent is in arrears, that money is due no matter how old the child is.
That is correct, they can get you for arrears at anytime. CS does not figure in to your FICO scores. I have 2 sep TL's pertaining to CS. The only time it has been an issue is when I re-financed my house. They counted it as a debt and it figured into my debt to income ratio.