OP starts out with an incredibly ambitious itinerary that involves spending most of the available daylight hours sitting in a car ... crossing international boundaries ... and involving five different languages (and road sign conventions) overall ... and four different currencies in the first three days.
Then scales back somewhat. But never having driven in Europe suggests it's no different than driving in the US.
It seems, unfortunately, the OP falls into what I would describe as the woefully misguided category ...
In terms of practicalities not already addressed, is the OP planning on renting a manual (stick shift) or automatic car?
Pricing differentials between the two in the peak summer months are likely to be quite significant ... Also what size vehicle is the OP proposing to rent?
Depending on the choices there, that is another factor to consider when it comes to driving ... and parking.
As others have suggested, focus on a couple of locations ... have an actual holiday/vacation ... not a stress-inducing time period trying to cram in too much in a short period of time ... and recognize you are going into completely new environments.