You can buy engagement invitation cards at most party shops. Instead of asking for cash only a good idea is to have a 'money tree.' It's a tree with branches only (you can get them at any craft store) with small close pin type pegs from the craft store and you attach the guest's envelope with the money in it. Later, the bride to be can open her cards. Thank you notes should go out no later than two weeks after the event. The sooner the better.
Technically you can if the amount on the card is $9.99 or lower. I actually was given a $100 Target giftcard but since I'm a disgruntled former employee I bought a bunch of $5 giftcards and had them...
I personally am not aware of any store that currently sales Amazon gift cards. As you know, you can buy them from the website directly or I just read that Coinstar offers Amazon gift cards instead of...