Engine run-on and knocking, pinging

The run-on (car runs after key is switched off) seems to occur only after the car is warmed up. The knocking, pinging occurs when I hit the gas hard at low speeds.

I've been told that BOTH problems could be caused by a timing issue.
I've also been told that BOTH problems could be caused by an octane issue.

Oh, the manual says regular gas is fine, but the car was stock with a two barrel and a single exhaust. I've put on a four barrel and dual exhaust.

There were a few other, less likely suspects named, but these two seem to be the favorites.

What say y'all?

Thanks.
Author: 69 Polara