Idk really. Anything that's anime related but wasn't intended to be in the actual anime
This is where madoka will end up after the balloons run out... cold and wet and alone
Not really, no.
The new character serves no purpose whatsoever, and it basically ignores everything that happened in the first season.
The books' author seems to want to do reset-button comedy, so when KyoAni went off and made a dramedy with an actual plot that only used the character designs and some scenes, they got all pissy.
Now it'd have been nice if KyoAni had said "tough shit: we bought this, you saw the contract, and we'll make what we want", but they didn't, so S2 (and the final movement of S1) is a pathetic attempt to squeeze their actually-decent story onto the front of a series of crappy LNs that don't go anywhere.