How does one make accidentals in atonal music apply
only to the adjacent note?  Also, in a case where an ostinato would clearly
state the key of d Flat in an otherwise atonal piece, should the accidentals
be stated as flats or sharps?  How does one override the default if
necessary in that case?

to start with, choose atonal in the key signature dialog; although this
behaves like C major. 

Input the notes in whatever way you like and then run one of the plug-ins in
the plug-ins > accidentals menu to tidy things up. There are four worth no
about.

Add accidentals to all notes
This puts an accidental on every note in the score without exception. It
takes its lead from whatever spellings are already in the score. EG: if
you've input an F-sharp followed by a G-flat, they will both be spelt that
way.

Add accidentals to all sharp or flat notes
This only adds accidentals to sharp and flat notes, and naturals which need
to be identified as naturals because they follow a sharp or flat in the same
bar.

Spell sharps as flats
This just respells every sharp as a flat.

Respell flats as sharps
Guess what! It turns flats into sharps.

As for using sharps or flats in an ostinato, it's really down to personal
choice. Give some thought to what is easiest for the instrument, but don't
forget that F-sharp and G-flat are actually different notes. In some cases
there is a good case for using a sharp over a flat.

A useful keystroke is Enter, which respells an note with a different
accidental. EG: F-sharp will become G-flat. This key also works on passages.

One last thing to mention is cautionary accidentals. These will crop up all
over the place if you start using the plug-ins above. A cautionary
accidental is one which will always appear, no matter what you do to the
other notes in the bar.