How do I backup Titanium Backup? I want to install Titanium Backup on a new phone and would like to carry over the settings from my old phone, which include current backup schedules. How can I go about this in order to avoid having to recreate them manually? 

I've checked the current backups and it looks like TB does not do backups of itself. I also have "My Backup Pro" installed, but it doesn't list TB as a selectable item for backup.
Go to the Titanium Backup settings page and enable (it it isn't already enabled) the Auto Sync TB Settings option. Then you should be able restore the file created on your SD Card to your new phone.