Putting it in park at highway speeds depends mostly on how new the car is. Newer cars will put the transmission in neutral and probably yell at you with the dash. Older cars the parking lock isn't strong enough to lock up the wheels at speed, so it'll grind and clatter or just break. Ruining the parking lock.

Turning the car off on the highway just makes you coast to a stop. Depending on if its an automatic or manual transmission; you might loose power assist on the steering if the engine stops spinning. Pulling the key out normally activates the steering wheel lock. Which is a whole other problem if you are still moving... Some automatics prevent you from removing the key if the transmission isn't in park though...

My driving instructor included #2 in the lessons a decade (or 2) ago

You lost power steering and power breaks, so car was heavy but steerable. Goal was to put it back in neutral, start the car, and drive off

TLDR, keep calm and carry on.

Not a gear head, but I had a friend in high school who was an idiot. While his girlfriend was driving on the main drag one day he stuck the car in reverse or park, not actually sure. We all braced for catastrophe, but nothing happened. The car basically was in neutral.

He also shut off the car while driving, but because it was in drive was unable to remove the keys. The driver had to shift to neutral, then she was able to restart it. Basically while it was off, there was no power steering, or power brakes.

ETA: this was in an 89 LeBaron.

1. Transmission would make a lot of noise, grinding kind, as the park pawl attempted to engage. It could lock up the wheel if it successfully engaged. I know because I've done this accidentally on an old 1970's car that had a shifter problem.

2. Nothing much - you'd lose power assist for the steering, and you'd have power assist for braking for 1 good stop. I've also done this.

don't you have to hold break to do either of those things?

1. From my understanding (this may not apply to all vehicles) is that Park works by engaging both a forward gear and reverse gear at the same time, effectively locking the transmission. So putting it in Park while driving is almost guaranteed to destroy the transmission. This is also why there's a separate parking brake, highly recommended to use if parking on a hill.

2. When you turn the key off, then all but ancient cars will mechanically lock the steering wheel, as a theft prevention measure, meaning you will be completely unable to steer. And no I don't mean the loss of power steering making it hard to steer, I mean physically mechanically locked, you will not be able to steer at all.

TL;DR - Regarding both questions, catastrophic damages and likely death 💀