Yes, all cars feel different. Even identical cars can feel different. Sometimes steering/clutch/brakes/accelerator are set slightly different on the same model.
But you get accustomed very quickly.
I'm always the designated driver of hire cars when abroad. Basically any kind of car can be allocated, whether it's a hatchback, estate or even a SUV, just depends what they have at the airport car lot at the time. Often the airport car park exits straight onto a busy dual carriageway or motorway so you don't really have time to acclimatise yourself. I just stay focussed, drive calmly, and concentrate on the car controls and before you know it, you're fine.
It really doesn't take long. Just make sure you know where the basic controls are and "just drive". Try not to get bogged down with "extras" such as the heater, radio, etc., which are things you can look at later. What matters are the gear stick, indicators, light switches and windscreen wipers - if you know where all those are, you're good to go.
As for size/parking, etc., just go to a quiet car park and practice a bit.
I actually passed my driving test in a car I'd never driven before the day of the test. The instructor had just got a new car, different make/model, and the only experience I had of it was the one hour lesson immediately before the test. Instructor just took me on a "dummy" test route to get me used to it and then did the usual parking, three point turn, reversing around a corner, etc., and it was absolutely fine. Passed first time.