Yes, it is appropriate to give a gift at a graduation party. The gift could be something that reflects what the graduate plans to do in the future. A college-bound high school graduate might receive some item needed for college. A college grad could get a gift that would help for his/her career/job or setting up a home. The same idea works for a high school graduate not intending to go to college. Another idea would be a picture frame or photo album for graduation day photos. It is not necessary to spend a lot of money.
at the graduation
* It depends why they didn't invite you. If it was a small graduation party and a very few people there or you live out of town then yes, send a gift, but if they simply left you out on purpose then don't give a gift.
No you don't give him a gift. It is your party and it's expected that your guests give you a gift. If he should ever have a birthday or say Graduation Party, then that is the time to give him a gift. Be sure to personally thank your friends for the gifts they give and let them know you appreciate it.
A camera, a gift, and a smile.
Yes
It was an honor you were asked even if you can't attend the graduation so yes, you would give a give. Only spend what you can afford and don't put yourself into debt over it.
It is customary to give a gift, but it need not be expensive. Be thoughtful and inventive. Include a nice card with your most heart-felt wishes.
If there is an engagement party then the parents would generally give a gift, but if there is no party then no, they do not have to give an engagement gift.
500,000,000
if you want, its up to you
See great thread on http://www.mamasource.com/article/is-a-graduation-gift-required
Mastercard is a great gift to give as a graduation present. Yes it is a good idea to give your sister a master card because this way she can purchase what she wants of her own choice.