Will the Output window show up in my final movie if I use a trace command?
No. The output window is part of the Flash authoring application and will not show up when your Flash movie is on a Web site.
What happens when I divide a number by 0 in ActionScript?
You get a special ActionScript value indicated by "Infinity". However, you should consider any division by 0 as a bug and avoid it.
Is there any limit to how many else if statements I can use?
No, but there is a better way to implement a long list of conditions. The case statement allows you to test one variable against a list of possible values.
If I place a function in one frame's script, is it available to scripts in other frames ?
Yes, as long as it is on the same timeline. Functions inside movie clips, however, can be directly accessed inside that movie clip only.