Can I install gaskets to the case-side rather than plate-side?

Yes, but only with caution.

First, gently place the plate into the case, and see where the plate lands against the case.

Then, place the gaskets to cover that exact area. 


This will allow for switching between various plates without installing gaskets on each; however, a misplaced gasket may compromise sound, feel, or function.

The firmware flashing log results don't match completely with the provided screenshots; is this fine?

As long as it reports that flashing is successful, types normally, and shows up in Via configurator, the firmware flashing process went successfully.