The first time I had an engine failure from the climbout demonstrated to me in the R22 was on my FI course. Come to think of it, that's was probably the first time I had an instructor with enough experience for it to be safe to demonstrate it!!!!!!!
In an R22 they don't last long, but with rapid and simultaneous lowering of the lever, application of aft cyclic and right pedal they're survivable.
Bear in mind the surprise factor here too, if it's for real. I actually found the demonstration quite an eyeopener. I don't pull the trim in the climbout any more...or do anything else; my left hand stays right on that lever. But to be totally and brutally honest, I still don't think you should place any bets on survival of an unexpected engine failure on the climbout in the R22...well, not if I'm flying it anyway.
Autorotate, brilliant post. I would agree - aft cyclic is essential to get all the RRPM you can; forward cyclic will reduce it. And RRPM is a lot more important than airspeed.