Alexander The Great

Beauty is in the eye of the beholder and much of ancient coins is a matter for interpretation. Personally a test cut is fine in my opinion if it doesn't obliterate key details. SO on the OP's coin or my Tet the tet cut are in a good place to the left of the portrait and nothing is really lost by having it there. However a test cut through the owls face on an Athens Tet would be a big minus for me since the owls face is key to that type of coin.

Just went through all of Price and did not find the thing (hard to tell what the monogram is) Given the obverse style I would tend to think that it could be from Magnesia, but really not sure

Nice coin

Anoob, could be a [monogram looking like a] M, but not sure. And if it was it would more likely be Abydus, but they also all have something under the throne. First thought I had is that it was a Π with a dot in it

Generally speaking, the drachms from Abydus are more commom but the most commonly seen "lifetime" drachm is from Miletos...