Do you have a DE filter or a sand filter? Because if you backwash a sand filter, DE doesn't come into the picture.*
But if you backwash a DE filter you must put more DE in.
*We do sometimes add a LITTLE DE into sand filters to improve performance, but it's not necessary.

Now I don't know what "overhaul" means when it comes to filters. If it's DE, I don't know if that means clean the screens in acid, replace/repair damaged screens, repair other mechanicals in the filter or what. If it's a sand filter does that mean replace/repair parts or seals in the multivalve, replace laterals?

There is annual maintenance on DEs, but usually not on sand filters.

There are directions with the K-2006C. You can ignore, for now (and, IMHO, forever) the acid demand test and base demand test, so pretend they are not there.
You'll want to test the chlorine for FC and CC (TC, total chlorine is the sum of FC and CC)
pH
Total Alkalinity (T/A)
Stabilizer (CYA)
and,
Calcium Hardness (CH)--but it's really mostly critical with concrete/tile type pools.

By far the hardest test to run correctly is the CYA test. The others are pretty easy.