Using the word oddities was fine. I didn't find it offensive. I think the reason for looking under your car at the driver's test is, as you guessed, to check for animals, children, etc. it's a safety precaution.

I'm pretty sure the right of way goes to the person either making the near turn or going straight. Aggressive driving can get you the win as well.

Regarding the automatic parking, I don't know how prevalent that is. Most cars do have a camera that activates when you put the car in reverse so you can see behind your car as you back up.