I'm fascinated by the fact that my takeaway is the precise opposite of what the author intended. To me, the answer to all of the questions was crystal-clear. Yes, you can academically wonder whether an orbiting space station is a vehicle and whether it's in the park, but the obvious intent of the sign couldn't be clearer. Cars/trucks/motorcycles aren't allowed, and obviously police and ambulances (and fire trucks) do…
It's still breaking the rule though. Legally I suspect it varies between jurisdictions whether the sign doesn't apply to them, it does apply but conflicts with another rule, or whether it's argued as an extenuating circumstance.
Then there's the edge cases like bikes and horses.
Are they vehicles? It's completely reasonable that they could be deemed to be.
We've got the same kind of argument going on with e scooters at the moment.
Ultimately I answered a lot of these based on what I would expect to see in a park, and what I think is reasonable. But they aren't objective measures.