E.g. you don't call it the front/back door, you call it the bonnet/boot (or maybe hood/trunk depending where you're from) though that probably is stretching the definition of a door a little bit... but then you also have nearside and offside for passengers/drivers side, though that's probably a bit more of a technical term.
It is, but then so is the stupid "3-door" / "5-door" / etc. car classification, which is really 2-door / 4-door / etc. with the trunk being counted as additional door for some reason.
“Driver side rear door” or “passenger side rear door” are pretty common, at least in the US and UK, where they mean the opposite.
“Nearside“ (passenger side nearest curb in a right-hand drive vehicle driving on the right) and “offside” (driver side furthest from curb) are also used in the UK.
I've the vaguest recollection that sailing/steam boats used to say which side to move the wheel towards to steer; that begging opposite of the way the boat will go??