MySQL database stops working after log enabled
You certainly have a problem but that does not look related to enabling general logging.  Are you sure it's not that those errors have been filling your error log previously and you only just noticed them after an investigation stemming from enabling general_logging?

Enabling general_logging can and cause your server seemingly hang.   General logging will log every single query thrown over the fence to mysql (even one resulting in syntax errors).

This can cause the file size to grow a lot more rapidly than expected.  Run

show variables like 'general_log_file';


Then check the disk usage for that path from the shell command line

df -h /var/log/mysql/mysql.log


If that reports 0 available and 100% use then it is very much expected mysql would hang.

It's the defined behavior of mysql when any log (general, binary, error) cannot be further written to because space has been exhausted.   The idea is it will just hang out until space is made available.

To remedy you want to either more the log to a filesystem with a filesystem with enough space, or just delete it if you don't care.  Then either restart w/ the general_log variable pointing to a file system with enough space for your traffic loads or add more space to the existing file system.