Wow, that's a lot of basic stuff and my first recommendation is to get a good book on basic photography. Someone else recommended John Hedgecoe's books. I second that and gave my wife one several years ago (it didn't help because she didn't read it--doesn't want to know anything about photography that she cannot learn thru osmosis).
The second is to take a class. If you live near a good camera store, inquire there. Some stores do basic classes especially after Christmas. If not a good shop, how about a local club, community college or the like? Classes are one of the best ways to learn because, unlike with a book, you can ask questions and have discussion.
To answer your questions above.....
To freeze motion you need either a high shutter speed or to have most or all of your light coming from flash (flash is very fast and will usually stop action). If there is ambient light too you can do some cool effects utilizing second curtain flash synch (don't worry about this right now) to show the motion.
If you are at your default ISO and cannot get the shutter speed you need, consider pumping up your ISO to higher levels. 200, 400, 800, 1600. Note that you are NOT making the chip more sensitive to light, you are just amplifying the signal so you will tend to introduce noise. In the film days going to higher ISO film meant introducing more grain. It's a trade-off.
AWB (auto) will work well in many circumstances. But if it is a critical situation, you can guess at the white balance (flash, incandescent, shade) and set it on your camera. Or, you can shoot raw and change it when you go to edit the image. Or you can use a tool like this to set a custom white balance.
http://www.photovisionvideo.com/target.html
These tools are expensive but you can be certain that your white balance and your exposure are ROCK SOLID. I have both sizes and use them almost every time I shoot critically. And, yes, I know these tools are not cheap. Nothing in photography is. Welcome to the club. I remember asking a clerk in a camera store one day why a plastic darkroom funnel was $4.50 instead of like $.79. His response, "because it has 'photo' stamped on it". That's the way it is.
When should you use built-in flash? Almost never. But if you are taking candids and you need some flash and that's all you have, then use it. Seriously, flash on camera is great but get a separate flash (420, 550, 580) and learn to use it. It takes some experimentation. Learn how to balance ambient and flash and how to use flash for fill and/or for adding catchlights. Again, this is a big topic.
Small apertures 2.8, 1.8, 2.0 indicate a bigger opening and they let in more light. But they also decrease depth of field (the range in distance from the focal plane of what appears sharp). This is great for portraits where you want to leave the background blurry so the attention is on the person.
Large apertures like 16, 22 and up indicate a smaller opening and let in less light. They also offer greater depth of field. These are good for taking subjects where you want your image to be sharp from front to back. Landscapes, architectural images, etc.
Note that DOF doesn't mean that everything that appears sharp is "in focus". There is still only one area that is truly "in focus" but varying the DOF gives you more or less distance in front and in back of your subject that is in focus. Here's an example of shallow DOF. I think it was shot at f 1.8 or something.
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I could have shot it at f 8 or something but this way the things I wanted to really emphasize, her eyes and lips, are the only things that are really sharp. Everything in front or in back is soft and it gets soft very quickly.
Here's an image of my cousin sitting in an old soda-fountain/lunch counter. I wanted to get the details of the place so I used flash to add some light to the gloom and I used a higher f stop so that more of the shop is sharp (appears in focus). The actual focus point would have been on her eyes.
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I hope this is helpful but I really do recommend the book and some classes. Or, go shooting with a buddy or two.
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