I have had a short break to think about this, and hopefully offer some helpful advice to recover from the ownership change.
First of all, if you haven't done anything else, you are just one bad command deep and haven't removed or damaged anything, so you can probably recover if done carefully.
First of all, from your list of changes I would do the following steps:
Code:
chown -R root:root /var/log
chown root:utmp /var/log/wtmp (If it complains post error here)
I really have no idea about the anaconda, gpm and afew others, but lets go with root:root and just be alert for errors reported later or on next boot, and handle them when they arise. All things considered you may get off easy! But if possible I would still recommend comparing it to a clean installed VM.
OK, back to mysql - it appears to me still that mysql has never been initialized. Just to be ABSOLUTELY sure, what is the output of (as root, or with sudo)...
Code:
ls -l /var/lib/mysql
AND
tail /var/log/mysqld.log
After that we can set up your mysql safely.
Hope this helps - let me know what you find!