Time Machine backups (2 backups at same time)
By default, time machine excludes external drives that are mounted, but you can add them back into your backup in Time Machine "options" (found on the Time Machine Prefrence Pane). See here for more info: https://www.macworld.com/article/3153995/how-to-make-sure-time-machine-backs-up-external-drives.html

To add an external drive into the list of Time Machine Backup Drives, just use the "Add Time Machine Backup Disk" in the Time Machine preference pane.

Regarding your Question (2), You can not direct a some of your backup to one time machine, and the rest to another, thought that would be a nice feature. I personally use an rsync script that runs nightly to solve a similar problem, though that's nowhere near as convenient (or user-friendly) as Time Machine.