There are tons of regulations that increase housing costs a lot. Doesn’t mean they all don’t make any sense whatsoever.

Car / inhabitant rate is about 58% in Germany, if you like it or not, and the rate is still getting slightly bigger, so no, most people have a car. Also the parking lots are usually being sold / rented out as an extra, that should at least in theory compensate the price for people without the need somewhat.

Underground parking is more expensive to build, but it’s not being built to blow up the prices, usually it is the only way to reasonably accommodate the parking necessary, also from a financial POV. I hope you are not proposing atrocious ground level parking for urban settings.