Isn't an engine-off (glider) landing a requirement to get a pilot license (in the US or everywhere)? I thought it was...
Same as a helicopter autorotation landing?
Kinda scary if it isn't. I would've thought loss of power would be one of the most common emergency maneuvers you practice for -_- . I'll be thinking twice if someone invites me... not that there's any danger of that happening but who knows lol.
It depends on your instructor. You will have to demonstrate one for the examination but it's up to your instructor how far you take the "approaches" during training. You typically never demonstrate one and actually shut the engine down, just at idle. Some instructors see that you made the picked out landing spot and tell you go around while you're still at 500 feet, others like my first instructor make you fly it to ground effect.
My primary instructor who was born in 1916, flew bombers in both WWII and Korea, and was a tough SOB to train with. If you took your hand off the throttle for a
second he would wipe it to idle and say, "where you putting it?". I couldn't scratch my nose without demonstrating an emergency approach. Spins & spin recovery? We weren't supposed to do them in the schools 152's but I got taught them anyway.

I firmly believe Peter's hardcore approach to training has saved my ass many times, but never so much as in 1998. I had an engine failure in a Cessna 172 at night. The survivability of night emergency landings as a percentage is in the low single digits. Later on I went and looked Peter up and told him what had happened and thanked him for being so tough with me during training. He had a "satisfied" look on his face, although he did say it wasn't a
real emergency until you had dead guys on board, at least one engine out and holes you could pass your leg thru in the aircraft.
US flight training is actually woefully inadequate with regards to stalls and spins. It's not even part of private pilot training and IMHO that's stupid. Yet stalls/spins still kill pilots every year.
The difference with rotary versus fixed wing engine-out landings is, fixed wing might get you somewhere other than directly below you, but you'll have to land with forward speed and need an open area. Rotary wing will put you almost straight down but you can land with little or no forward speed.