See the Clinic Concept, and the rest of the Introduction.
See the History, as part of the Introduction.
See the List, and see the History.
You can print these documents, and you can look at the reports from previous clinics.
All clinic files are in http://math.ucdenver.edu/clinic/... See the document list for relevant html files.
You must learn it. You will have some class time allocated to this, and there are many resources available outside of class, including your classmates who either know LaTeX or must also learn it. If you go to any research environment, such as graduate school, you will find LaTeX necessary. More generally, you will find it useful.
Some clinics will let you do that. It's up to the teacher. However, working with a team is one of the educational benefits of our clinics, so you will be at least encouraged, if not required, to work with a group (typically, three to four) of your classmates.