Kristy-
First of all, these are some tough questions, and I think you're taking the right approach. First of all, let's dispense with the impossible/improbable...the response of "Get a 5D Mark II and a 70-200 2.8 IS Mark II" is not a reasonable solution for you. 
So let's talk about the SX20is, assuming you're going to get one, and your particular shooting scenarios:
Let's talk about the graduation outside, because it's easier. The SX20is will allow you to shoot from the bleachers with its "20x optical zoom." I implore you to keep the "4x digital zoom" turned off. It may give you the supposed advantage of more reach, but the picture quality will leave you very upset. With being outdoors, you'll have the advantage of having enough light, and you should be able to generate some nice clean images.
The shooting in the auditorium is a different story. You've said that in the past, your images have either been too dark, or too blurry. These, of course, are elements related to exposure and available light. Since I don't know how much you understand exposure, and I don't want to talk down to you, I won't make any assumptions.
So the only advice that I have is to try and set your camera to as high an ISO as you can get away with. Though that camera has ISO ratings of 80-1600, I wouldn't expect it to be noise-free past ISO 200, and I would imagine 400 to be "usable" but noisy. Once you hit 800, forget about it (IMHO.)
When you get your SX20is, I would perform the following experiment: shoot some shots around your house in "P" mode or in green box mode at ISO 200, 400, and 800. See if you can deal with the graininess of the pictures. That what you'll know the top end of the ISO that you're willing to deal with.
If any of this is confusing, I'd be happy to answer more questions for you. I'm an amateur myself, who is still learning to take better pictures. Shoot me a private message with a little bit more about how much experience and technical savvy you have, and we'll talk 
Good luck!