When SPC/E water model is used along with Shake for bond and angle
constraints, then do the forces in the dump file on water atoms
contain any contribution from constraints or only forces due to
non-bonded interactions with other atoms ?
Only contributions from non-bonded interactions.
You can monitor it, at least the energy, using thermo_style multi, or another custom output which outputs intramolecular interactions. These should be zero, if shake is applied.
Dump files are written at the end of the timestep, so they include
the constraint forces. The fix store/force command will store
forces before constraints, so you can also output those.