1) No. GR is calculated at game end only. This is a weakness of GR, although a solution to fix it isn't obvious (other than CDed players should count as having been eliminated).
2) This is because a loss in GR is always the same proportion of your GR score (wins are scaled by your opponents, but losses are not). This is another weakness of GR.

I've been working on a better system (with measurably less error in predicted game outcomes), but it's difficult to create a system that doesn't have perverse incentives (like, it's good for everyone to gang up on the high rated players, or it's better to throw a solo than to be part of a draw you're not in). I'm reluctant to change to a system with different incentives to the base scoring system (1 for a win, 1/drawsize for a draw, 0 otherwise).

I see.
In the case of losses always being the same proportion of your GR score, then wouldn't everyone that has played one game and lost have the exact same score?

Yes, exactly.

Was there ever an official response to the question of when (or if) category GR will be updated?

It should be better to throw a solo then let yourself be eliminated from a draw

Just for the record

Or at the very least equal, certainly not a perverse incentive.

Fixing the other perverse incentive of ganging up on high-rated players should be solvable by not varying any player's rating change according to the performance of any other individual player. I can't really think of a reason to have such variance in the first place.

So, are we basically recreating Elo/TrueSkill/etc. with non-binary game outcomes here, or what?

Er. That last was maybe a bit dismissive in tone. But the constraint implied by that perverse incentive should simplify, rather than complicate.