Yes, you can.
If you're in the US, no, a child cannot sue his parent for child support (payment for child support is not due to the child).
If the custodial parent agreed to deviate from the original child support amount, she can increase it back to the original amount if there is a court order. In additional, the non-custodial parent may have to pay back child support for the time when he paid less.
yes
It is likely that the judge will enter a child support order and may assess an amount for back child support.
You have to pay the amount of child support ordered by the courts. The only way your inheritance might come into play is if your ex decides to take you back to court to get more child support.
If the amount owed exceeds the threshold, no.
It is dependant on which state that you live in as to if the children are entitled to back child support after they are grown. You will need to consult with your local state child support office so they can better assist you with this question.
No. The back child support is owed to the custodial parent and the amount due doesn't go away until it has been paid.
It happens. However your child support obligation may be offset by the back child support you are due unless that amount has been forgiven by the courts.
It belongs to the child.
A "purge" means that if you pay a certain (court ordered) amount of money towards your back child support, you will not be jailed or, if in jail, you will be released.
If there is a tax return.