Change path for binary logs and scheduling
You should be able to set the binary logs to a new partition by providing the absolute path:

log-bin=/my/other/dir/mysql-bin


You might need to copy the old binary logs to the new directory and update the .index file with the new path information (Do this only when mysql is not running).

Why would you only want to binary log during certain intervals of the day? Doing this could really mess with your ability to restore at any given time.