You don't have to free up space on the drive. Time Machine does that all by itself, no need to worry about it. And you should never EVER manually delete folders on your backup drive. That will destroy the integrity of your backup and basically render it completely useless.
I would suggest ejecting the drive, unplugging it, and rebooting your Mac first. Then plug it back in and try to backup anew. If it still keeps throwing error messages report back but chances are the reboot will end up fixing it.
At the end of the day Macs are only computers.