If a changeling in D&D 5e shapechanges into a merfolk, would it get the abilities of the race, for example, the ability to breathe underwater? I have been wondering about this for ages, and haven't gotten a straight answer, because the race profile for the changeling doesn't talk about this sort of thing.
None of your game statistics change.
The changelings Shapechanger feature says:
You can make yourself appear as a member of another race, though none of your game statistics change.
This means if you can’t breathe underwater, you can’t breathe underwater when you use Shapechanger.
Game statistics here refers to everything mechanical about your character. That is, all of your racial traits, class features, ability scores, everything. We see this explained for NPCs in the Monster Manual:
A monster’s statistics, sometimes referred to as its stat block, provide the essential information that you need to run the monster.
But this applies to PCs as well - your statistics are everything that make you, well, you, within the calculus of the game rules. In the Player’s Handbook, we have reference to game statistics in the step by step character creation section:
Your character is a combination of game statistics, roleplaying hooks, and your imagination.