The install script (the one giving the errors) is telling us that your DB tables have a prefix "zen_"
The uninstall script has no such prefix which means it isn't uninstalling what it needs to.
The zencart sqlpatch code normally takes care of this (I think) but if you are running it via phpmyadmin (or similar) you'll need to edit the uninstall script by adding the prefix.
Not difficult. Where the script reads
FROM xxxxxxxx
Change them to read
FROM zen_xxxxxxx
There are five lines that you'll need to change.
The 500 error is another story. Although it can be caused by many things one of the most common causes is folder or file permission. Only your host will be able to tell you the exact cause.