Answers to generic questions:
1. When I wrote mine, I focused on one/two topics. Trying to write about too many things just dilutes your point and makes for a less convincing argument.
2. Depends. Usually more is better, since you can elaborate on things, but this is not always the case. Just write as much as you need to get your point across.
3. You can do both - you don't need a full-blown introduction to get you rolling, especially in a short-essay format.
My essay was essentially a (purposefully) overblown version of why I should go to Mudd, emphasizing why I would fit in. It turned out to be quite funny to read, actually, but it helped get the personality through.