Engine revs fine in park, but not in neutral, lunges, loses power

1. My car has started to completely lose power when you accelerate too quickly. Engine won't rev, no acceleration. I can turn the car off, let it set for a few seconds, and turn it back on and it's fine. 2. Sometimes when you accelerate there is very little power and then it lunges, but it won't hold a steady speed. Turn car off for a few seconds, turn it back on, and no issue. 3. I can rev the engine when it is in park and it is a smooth acceleration form 1000 rpm's up to 3500+ rpm's, but if I put the car in neutral and start accelerating, the tachometer starts to bounce around 1,500-2,000 and never stabilizes. It doesn't matter how far I have depressed the accelerator.