How fast should you accelerate and what's a bad range for the RPMs?

I accidentally downshifted from D4 to D3 once and then D4 to Neutral once, how bad will that hurt your car?

Then another time, I didn't know I was in 2nd gear and I was going 60, also bad?

Then on another time again, I didn't know my car was on, so I turned the key again and it made this screeching noise...

So tell me, what will each situation do to the car?