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.

Yes. Given the nature of the item and spell, and given that how they interact isn't explicitly written and therefore the rules put it on the DM's shoulders to decide, how your DM handled it was correct.

The item

Without spoiling too much, a bard's instrument that:

• involves “attunement”
• is able to cause psychic damage to unattuned players

… matches a specific magical item in the DMG's list of magic items.

For those who want to be spoiled, they can read about it in

the DMG on page 176.

The interaction

Whether using a mage hand to play the instrument counts as personally playing the instrument, at least enough to suffer the damage, is in the realm of DM's judgement. There are no rules for how the item interacts with "indirect" playing, so the game falls back on the basic rule that the DM decides based on their best judgement.

Since it's psychic damage and the mind doing the playing is the rogue's mind operating the spell, I would agree with your DM's call. In another game with another DM though, the damage might just fizzle out with no available target instead. Another method of indirect playing may also have a different result — for example, building a machine to strum it would seem (to me) to not count as the builder playing it, but using a stick to play it would. Again, this is explicitly down to DM's judgement, so your DM's call is supported by what the rules say is up to the DM, and I think the call is pretty reasonable.

(And aside, isn't it way more interesting to discover this? That's another, separate reason to appreciate the DM's call here!)

A saving throw

Normally a saving throw is required before suffering this particular damage. If the DM skipped it entirely, that isn't (normally) their call to make and a save should have been rolled.

It's possible that the DM forgot, or maybe rolled the save for you. (I'm generally fine with making rolls for players when it's done to preserve a good mystery. If it was me that would be likely why you didn't roll, but I don't know your DM's habits.)

If the DM simply left the save out, that's something that could be corrected next time. A nice non-intrusive way to do this is to ask "don't I get a saving throw or something?" This nudges the DM if they forgot, without the player engaging in "backseat DMing".