I think I know "handbrake" from racing games, but people here in North Carolina usually say parking brake instead.
Fakedit: Oh yes, and emergency brake is common here too!
I remember worrying my brother by resting my hand on the lever. In my car it's between the seats, though in some vehicles it's a smaller catch-lever below the wheel near the door. Manuals don't have a "parking" gear, see, so you have to activate the brake separately.
My mom had a habit of activating the brake then also leaving the car in gear. She grew up in the mountains, see, where it was customary to do that. The idea was that if the parking brake wasn't quite enough, the inertia of turning over the engine would help.
Which is how jumpstarting works! I've managed to jumpstart my car a few times just by pushing it up a small slope with someone's help, leaping in, and putting it in gear. The engine's turning over fast, the alternator turns that to voltage, and that's just enough for the spark plugs to ignite. Then just drive it around for a bit until the battery's charged!
I'm still not actually clear on how that works for automatics, heh. I guess it's fundamentally the same. Diesel engines, on the other hand...
I do not find it weird and I have never driven a car. Only bikes.
But I do know that to be an effective driver, you would need to drive on instinct as that will decrease your reaction time. Which would probably feel like you describe.
Ooh I didn't get my driver's license until I was about 20 and I cycled a lot instead, so that might be why I appreciate the haptic feedback so much. My poor steel touring bike... I really need to tune it up a bit, on the rare occasions I take it out I can feel several things wrong. Heh but it has friction shifters which are extremely robust. For the uninitiated: The shifters are analog levers rather than digital pre-calibrated selectors. If the chain grinds, you nudge the lever until it stops. Haptic as heck~
I'm still really proud of the time my alternator failed and I biked to the auto parts store to pick up a replacement, carrying it in a pannier - bag attached to metal scaffolding on the back of a bicycle. Auto-repair kinda scares me, but between Youtube and bicycle repair tools I was able to replace the part just fine.