Can I back up one external hard drive to a smaller external hard drive via Time Machine?
Question 1:
The short answer is 'yes' so long as there is room for the data.  But:
Time Machine will backup your system disk plus your 10 GB disk to another disk which has is large enough for the data you have plus space for future changes.
You might consider benefits of using Time Machine for just your system disk, but to use something else for backup of your external 10TB drive.  Examples I would recommend are Carbon Copy Cloner and Chronosync. Using Chronosync in a one way sync is appropriate if you occasionally (or frequently!) reorganise your data - this is not Time Machine friendly.
Question 2:
Only you can answer that as it depends on how much data you expect to add.
A longer answer is that you would seem to be a good candidate for using a NAS.
Caveat: I have attempted this answer with the assumption that your only disks are internal system disk and the two externals.
Aside: For always on continuous use I prefer a mains powered disk (desktop) over a bus powered (portable) hard disk drive.