No problem, ms.yt
When it comes to the shadow edge of light, here's what you need to know. The farther and smaller the light source is in relation to the subject, the harder the shadow edge will be. The opposite is true; the closer and larger the light source is in relation to the subject, the softer the shadow edge will be.
Take, for example, the sun. The sun is HUGE, but in relation to a person on earth, it's just a tiny blip in the sky. So, a light source that small creates very defined and dark shadows. On an overcast day the light scatters through the atmosphere and clouds, so the entire sky is a light source (like a giant light box), so it produces soft shadows.
Another example, a desk lamp or flashlight aimed at your face from across the room will create hard shadows, because compared to you, it's a small light source and is very far. However, if you take that same desktop/flashlight and place it an inch away from something small, like a toy matchbox car, it will create soft shadows because in relation to that subject, it's a large light source and it's very close.
Another thing you wanna know about light is a little something called the inverse square law. What it says that every time you double the subject's distance from a light source, the amount of light hitting the subject will be reduced to just one quarter (1/4) of what it was before. Double the distance = 1/4 the light. So, light falls off very quickly when you're close to the light source. A child standing a foot away from a window (the light source) will have four times the light hitting her than a child standing just two feet away from the window and sixteen times as much light as a child standing just four feet from the window. Think about that for a minute. Three feet of difference isn't very much, but it results in a very dramatic reduction in light, because they are very close to the light source. However, two children three feet apart from each other, but twenty feet from the window, will not be as dramatically different from each other, exposure-wise, as the children who are near the window are to each other.
So, one way to control the strength of light, aside from adjusting the power of the flash unit, is to vary its distance to the subject. But, as previously explained, moving a light further away in order to reduce its strength can also make the light "harder". If you're using a key light and a fill light (or fill reflector), it's easier to move the fill around to get the light ratio you want. That's because the key light will create the primary direction of light and shadow, and mask any harsh shadows that the fill would create if it were the only light source.
I think based on your tips, that my main problem is having the umbrella too far from the subject. I really had no idea where it should be. Thanks for the tip about the distance from the background, too. I should have realized that. I am having to deal with flourescent light in the room, and yes, I'm just looking for "normal" senior pictures. This is primarily for the composite picture that hangs on the school wall, so I can't get too creative. 
