1. This is a humble question: does the elevator weight have a purpose
other than balance? Does it have any connection with flutter, or is
flutter more a function of excessive control mechanism backlash combined
with velocity?

The weight is ALL about flutter. As a gross simplification, the
control surface CG acts like the aircraft CG, further aft de-stabilizes
the surface. The actual mechanisms are many and complicated.

2. For a serialized production glider, is the control surface balance
weight amount the same for each glider, or is it tuned for each
individual surface, making surfaces non-interchangeable between gliders?

There are control surface weight and moment limits set for each model,
these are in the repair manuals. When any repair work is done on a
control surface, the weight and moment must be checked to be within the
limits, or the aircraft is unsafe.

Todd Smith
3S