Are drones allowed on the property and if they are could I fly it to watch a game?

It's a distraction and a potential safety issue. I highly doubt they would allow it.

Certainly not over the field of play on ANY field.

As an umpire, there, I would not allow it

Doubt it ...

I definitely would not think so. Ask. Maybe there is a place close by that you can fly it up and zoom in from drone. Without it going into the park.

No

I doubt it.