[RPG] How does the Dragon’s “Solitary Shapeshifter” characteristic work

Stat Changes

It seems very clear that you apply no stat changes.

This ability functions as a polymorph spell, the type of which is listed in the creature's description, but the creature does not adjust its ability scores (although it gains any other abilities of the creature it mimics).

There are no qualifiers here -- it says the creature does not adjust its ability scores, so it doesn't! The part of polymorph that you're looking at says that you

adjust its ability scores to one of these two sizes using the following table

This is exactly what the change self ability tells you to ignore.

Even though it doesn't use the word "adjustment" in the actual text of alter self, the word would generally mean any change to your stats. (And it would be a bit weird if shifting into a smaller form increased the strength of a Titan.)

Other abilities

There's nothing here to modify how polymorph spells work:

While under the effects of a polymorph spell, you lose all extraordinary and supernatural abilities that depend on your original form

Note the qualifier. You only lose the ability if it was contingent on your original form. In many places the DM will have to make a judgement call on whether that applies. But obviously, say, a manticore that shifts into human form can no longer use its Spikes special ability. The rule is intended to rule out nonsensical situations, so the change shape ability doesn't alter these rules at all.

RAW, it seems you quoted the relevant part of the rule already.

Destroy Water. You destroy up to 10 gallons of water in an open container within range. Alternatively, you destroy fog in a 30-foot cube within range.

The serpent form is not water in an open container or fog, and again RAW, should not be subject to damage from the spell. Spells don't generally do more or less than they say.

That said, this also seems entirely in keeping with the idea behind the spell (the spell destroys water and the target is water, a stretch but not by far), and D&D 5th Edition is by design more open to DM interpretation than previous editions. This seems like a case of the DM deciding to reward a player for creative use of their abilities, and s/he resolved that use appropriately.