Is there any way to draw on top of existing objects?
Yes. Just draw everything in a movie clip. You can use swapDepths to ensure that the movie clip is in front of all other objects.
Can I create other common Flash shapes such as boxes with rounded edges and circles?
Yes, but you will have to do it using the lineTo and curveTo commands. No other methods of drawing are supported.
How do I get rid of movie clips that I have created?
The removeMovieClip command works with movie clips created with the createMovieClip command.
Do I need to know the width and height of the text field before I place any text in it?
You need to provide width and height in the createText command, but if you set the autoSize property of the field to true, the field should size itself to fit your text.