Interesting questions. I'm not too experienced in tagging in this situation, but here are a couple thoughts from me:
- If you have accurate info, I'd suggest using drive_through={no, yes, only}. Looks like all three are used regularly: https://taginfo.openstreetmap.org/keys/drive_through#values
- I would consider leaving out the name= on most of these. (Test: "Is this ballot box itself named Amboy Middle School?")
- I'd say amenity=polling_station, polling_station=ballot_box is the best way to represent these, so good job on that!
Just my thoughts. Thanks for your contributions!