if custodial parent dies, does non-custodial parent get custody? ?

Usually custody reverts to the non-custodial parent, but there are circumstances where it's not true.

Did the non-custodial parent waive their parental rights?

Did the custody arrangement say something like "shared parental responsibility"?

Did the non-custodial parent pay child support?

Was there a will which specifically gave custody to the grandparents?

As I said, usually custody reverts to the other parent. There may be extenuating circumstances where it doesn't, but that's the norm.

Usually the non-custodial parent gains custody.

If the other parent has any rights at all then that parent will likely become the legal guardian as that parent is the next and closest of kin. You cannot will your child away from another parent who has their rights still in tact. No court would uphold that unless they could prove that the parent is a danger to the child. You would need the genetic father to declare that they do not want the children (self/court termination of parental rights) in a written and legal document signed and notarized by both of you plus a lawyer would be best. If you still took child support payments from an absent, abusive or otherwise financially or emotionally responsible father then you cannot take away his right to have the child after your death.

Sometimes the case is different states, different answers.

Don't know if it's automatic. What if the custodial parent put something specific in their will? If the non-custodial parents doesn't get custody automatically, can take it to court. Courts love to place kids with parents unless they're really unfit.

Yes non custodial parent is first in line unless theres some legality preventing custody, then original custodial parents are first

Typically all depends on how it is written out in the divorce papers. Try this site it might help you. ALLLAW.COM

yes that is usually the outcome.

only if there is no will