Yes, you can share your Amazon Prime with upto 5 family members. I have 2 of my neices and a sister on my account. They don't get free TV or benefits of loaned Kindle books, but they do get free shipping. Totally worth it if you can do it as a group buy within family. Or just make it as your Christmas gift! Add them to your plan as your gift!
We recently started watching Amazon's instant videos after getting Roku, but the main reason I never got into watching it on my computer was they don't have the selection that I would watch. Much of their stuff is geared towards Sci-fi or the movies that I'm not interested in.
ETA: I should look into Amazon student account. My daughter did get free membership this year because she started her college. But I thought it was just one year deal. Didn't realize that it's 50% off for later on.