D-76 stock can be reused. The development time must be
extended to compensate for the partial exhaustion of the
developer. D-76 can also be replenished using the
replenisher, which I think is still sold. I would not dilute
used developer.
   I can't be sure what it is the developer but a good
guess is that its particals of gelatin from the film. You
can filter it using coffee filters in a large funnel. If not
filtered the particals may be deposited on the surface of
the film during development leaving marks.
   A Brita filter will remove some chemicals from the
water, particularly Chloramines, which are now commonly used
instead of Chlorine for treating drinking water. Chlorine is
removed by boiling, Chloramines are not but are removed by
activated charcoal filters like the Brita. However, they
seem to have little effect on photochemicals.
  If your city water is questionable I would use the Brita
filter and also boil the water. Boiling it for five minutes
and then let it sit and cool. Then decant or syphon off the
clear water. Boiling drives off dissolved gasses and removes
some minerals. Don't use an aluminum or copper container,
both can get into the water and cause fogging.
  For small volume work D-76 is best used diluted 1:1 as a
one shot developer. The longer development time is also
helpful in getting uniform results particularly with films
that have development times shorter than about six minutes.