Great assignment and I’m really happy to hear you’re aware of the problem of lighting with this photograph.
There is so much to learn about lighting. It’s such a fascinating subject.
For starters I want you to watch the following 2 videos
http://www.youtube.com/watch?v=A6JFVHRwJwc
http://www.youtube.com/watch?v=mwqNRqDx680
These videos do a good job of showing the dramatic impact that lighting has your scene. Although the videos above are related to filmmaking, the ideas are exactly the same for photography.
In your “beauty” image, you have a harsh shadow caused by your flash. However, you bring up a good point: You mention that you can’t always control the lighting in a situation. And you’re absolutely right in most situations. However, when shooting indoors there are options available for you to play around with.
Let’s look at possibilities as it relates to your “beauty” photograph. For starters, the image is very close to the wall. Shadows will become less exaggerated and harsh if you pulled your subject out from the wall. The further away from the wall, the less harsh the shadow will be.
Alternatively, you could have lit the subject using side lighting and then turned off your flash. This would have eliminated the shadow and you would have exposed more shape. Flash lighting is “front lighting” and front lighting always strips the photograph of it’s shape.
Another ideas would be to get a lamp and shine the lamp on the background. This would also eliminate the shadow and would have allowed you to continue using your flash.
The idea is to play around with different lighting situations. For starters just use household lamps, overhead lights or flashlights. The main idea is just to experiment with the impacts of lighting.
Great work though. Keep up the good work.