Ptolemy (I Or II?) Ae Zeus-Ammon Right/Eagle Left Open Wings

You may be right, Susan. Ptolemy I and Ptolemy II are best matches by my estimation, and the HP (or pi-P) monogram on Sear 7763 can also be seen on yours. There really isn't enough inscription detail visible for me to be absolutely sure.

No, because we don't actually know what the various coin denominations were called. It's 27mm diameter, and made of bronze... so it's called an "AE27". This is true for virtually all ancient bronze coins in the "Greek series".

Coins about this size with the same design (Zeus/Eagle) occur regularly throughout the Ptolemaic series, but attempting to link them all together and tagging them with a name is speculation - we simply don't have anything in the way of contemporary records saying "the larger copper coins the king had struck were called whatzits, the smaller ones were half-whatzits".

It's possible they fit somewhere on the Greek drachm-obol-chalkon scale, known to be in use in a very few places which actually wrote out the denomination on the coins themselves, but assigning a name to Greek bronzes generally isn't done.

Being a generalist, collecting both ancient and modern, I tend to be a bit harsh with grading ancients myself, preferring to apply the "one grading scale fits all coins" theory. If it were mine, I think "Good" would be the best I would assign it.

Realistically, ancients are normally graded on a more lenient scale. "Very Good" would probably be an appropriate grade for this coin; I think the near-lack of legend would preclude it from "Fine".