Hi, Linda, welcome!
Neither of the two log files contain a clear error that shows why the backup stopped. They stop in radically different places, one at the very start, one at a step break well into the file archiving process.
When you upgrade Akeeba products, the program files are upgraded, in rare cases the supporting database tables are upgraded, but the settings and data are not touched. If you uninstall, then all settings, data and possibly locally stored backup archives are lost. So you only want to uninstall in extreme circumstances.
The 500 error on the fof library suggests that something may be wrong with your installation. So the first step is to reinstall and see if we can fix that. Please download Akeeba Backup Pro and install it twice, back to back, without doing anything else in between. The install twice trick usually works around a Joomla! installer bug that can fail to copy some files during installation or upgrade.
You can bypass the automatic backup on the Joomla! upgrade by disabling the System - Backup on Upgrade plugin. You really should have a backup before you upgrade, so let's try to get that going first.
Dale L. Brackin
Support Specialist
English: native
Please keep in mind my timezone and cultural differences when reading my replies. Thank you!
????
My time zone is
EST (UTC -5) (click here to see my current time in Philadelphia, PA)