Is it possible to install MySQL into just my section of a shared server, or does it have to be installed at the root and be server-wide? If it can be installed on just my section, then I can have MySQL on my site, otherwise I'll have to wait or look for another host. I'd prefer not to do the latter, if it can be helped.
It can definitely be installed and run by a normal user. The real problem is if your host allows it.
MySQL runs on port 3306 which is not a root-only port, and you can configure it to use ~/mysql/ as its path for everything...