Best way I found of taking the bend out is to use a large can and gently use it to work the curve out. For older cards made of thinner stock, I'll put them in a plastic sleave and tape them to a rolling pin. Works really well on the old cards and doesn't leave any creases or rippling.

No, they are not damaged. (At least not in most instances.) Bowed cards are most often caused because one side is coated and the other side is not. Autograph cards and sketch cards often fall into the category because one side has to be uncoated to sign or draw on (but it depends on what the other side is coated with, as well as if the card is exposed to humidity). The uncoated side bends inward, the coated side does not.

If you keep your cards in an air controlled environment, it is less likely to happen, but changes in humidity inside still occur between summer and winter, so it can be tricky.

There are other causes as well, but the coated side, and uncoated side is the most common, especially after UV coating came along. Some coatings (like varnish) still let moisture through, but UV does not. So older cards that had a shiny varnish on one side and uncoated on the other did not curl near as much as a UV coating on one side but not the other. I had a set of Classic Pulps which had a beautiful coating on one side and not the other, and every card in the set is bowed. It's still a great set though. That particular box was not shrink wrapped and arrived on a hot summer day, and so....