Yes, parents often go into debt. It is expensive to raise children.
the debt dies with them... you owe nothing
Minors cannot legally contract for a debt. Only their parents/guardians can assume that responsibility. So, your parents ARE responsible. On the other hand, if you are legally an adult and contract for debt - and your parents 'assume' responsibility for it -there would have to be legally binding paperwork naming them as the debtors in lieu. Simply giving their word is not sufficient, and you would remain responsible.
The estate.
The debts of the parents are paid by the parent's estate, not their children.
No, you are not responsible for their debt. The only person legally responsible for a debt is the person that signed the contract for the debt. It doesn't matter if your dead parents left you money. Collection agencies cannot legally collect someone else's debt from you - but they will try. See the FDCRA to know your rights in debt collection.
I don't know all of the facts, but I do that if the child is dead, the parents or legal guardians will be liable to pay off the debt.
Making a credit card would be forgery and illegal. A minor is not able to sign a contract and is not allowed to incur debt. Their parents may give them a card, but the parents are responsible for the debt.
Not unless the parents are a party to the agreement such as a co-signer.
In reality, if there is no written proof of the debt, the estate cannot collect.
Not unless they were guarantors of the debt.
It's great that you are attempting to help your parents with their debt management by the way of credit score advice. You could first help them assess what bills are causing the biggest strain on their pockets and from there attempt to down size.
Not unless said children have made a written or verbal agreement with whomever holds the debt to repay monies owed.