2) It's good to have a semanticly sane code base with all the common pages elements factored out into templates, but it's not a requirement. If it ain't broke.
3) Involve the community. Have a poll asking your users what to fix first, and start from there.
4) With a copy of the database, you can start developing the site using better technologies and processes; invite a few users to test the redesigned site, preferably on another machine. Report back to the community, publish a newsletter, show screenshots, etc.
5) Don't fuck with that database. Don't lose the server logs.
Good luck.