Does it damage an automatic transmission the harder you are on the pedal? Also, overdrive question?

I've always been really easy on my car. I would normally accelerate slowly or if I knew the car was about to shift I would ease up on the gas. I don't know, I guess I felt like it would be easier on the tranny if things were turning slower. Is that a false presumption? I know have a car that I'd like to have some fun with (but need to last). My question is, wear on the engine aside, would giving it a good amount of gas during shifts do any damage to the tranny? Does it really affect it in any way or are transmissions designed to compensate? Also, I've never had a car with overdrive. I'm usually driving without it but was wondering if it was ok to switch to overdrive as soon as I attain highway speed? How do I properly do this? Do I need to let off of the gas, or can I just press the button? I'd imagine doing it the other way around (ie shifting OUT of overdrive to pass someone) would be bad for the transmission? Thank you for the help!!