You seem to be confused. The fed is not part of the government. It was created by the government, but is not a part of it. The federal government is in debt, the fed creates debt.
The fed could buy up all the debt in the world, sure, but that wouldn't do anything to relieve the US Federal Government of it's debts. It would just owe money to the fed instead of to whoever currently owns the debt.
Moving around debt isn't the same as paying it off.
No, I'm not confused at all, but it appears that you are. The Fed does not NEED to create debt to create money, although that is how they do it now.
If the Fed felt like it they could simply credit the US government $20 trillion dollars and wipe out all existing government debt. This would be a terrible plan, but it's certainly one they could employ if they wanted to. As Milton Friedman famously mentioned if the Fed wanted to they could print wads of bank notes and fly around dropping bags of them on the populace. This would be a simple, straightforward increase in the money supply with no additional debt attached to it. The only problem with this is once you do it you can't take it back if inflation goes nuts, which is one reason (of many) that we don't generally do that.
Can you point me to what source told you that the only way money can be created is through debt?