Is 500 mg of amoxicillin 4 x day for 7 days enough to clear a dental abscess?

Maybe. Adequate duration of therapy has not been clearly determined for most infections, and we often make guesstimates. I would imagine that if the abscess was drained, no underlying tissues like bone were involved, that this regimen would be adequate.
Sometimes. Amoxicillin is usually a good starter, bt sometimes a stronger antibiotic is needed, such as clindamycin.