The driver will wait for us in/at the parking lot. All I know is that in the US, the 99.9999% assumption would be that the driver is waiting in the vehicle. If he's not, then that would normally need a special explanation. And there isn't one here. So if the vehicle is in the parking lot, he is in the parking lot, by extension.
After all, we drive into the parking lot. The parking lot is also a two-dimensional area, but it can be three-dimensional if the parking lot is enclosed (with a roof), which adds the notion of "height." In any event, I don't find "parked on the parking lot" incorrect.
The term 'car park' is derived from the military expression 'artillery park', which was a field or open space where guns were ranged. 'Car park' covers any place specifically set aside for cars to be left temporarily. It is a broader term than 'parking lot'. 'Car park' includes underground and multi-storey car parks, neither of which could be described as a 'parking lot'. Another point is that ...
A parking space is a space which is used for parking. Space is countable in this usage, and parking is being used as an adjective.
It would probably, depending on the location of parking near the post office, imply that I was parked on the street in front of the post office, but I wouldn't utilize those sentences to communicate that fact.
Saying "There is a parking space" is pretty useless by itself. It just says "a parking space exists". You do need to indicate it somehow or you're not being helpful to the other person. You need to either point to it or tilt your head or turn your gaze toward it or describe it somehow. - There's a parking space over there to the left. - There's an open parking space in the next row.