How do I remove files from my Time Machine Backup and then how to exclude external hard drives from Time Machine?

For deleting backups from Time Machine: http://pondini.org/TM/12.html

For excluding things from backups: http://pondini.org/TM/10.html

For general Time Machine advice (all courtesy of Pondini): http://pondini.org/OSX/Home.html

External hard drives (except Thunderbolt or eSATA drives) are excluded automatically unless you remove the exclusion. Exclusions are managed in the Time Machine preference pane by clicking the Options button.

You're welcome.