1) It is not necessarily true that the GM's role is of "impartial arbiter between the rules and the players." That's one playstyle choice. Please let us leave room for other playstyles in the discussion.
That's the role the DMG defines (pg. 5) and is as a result one of my DMing principles as outlined in my second post in this thread. Stating what the DMG says and saying what I do is in no way shutting out discussion for other "playstyles."
The DMG doesn't say impartial arbiter though it says mediator...
Pg. 5 - "Dungeons & Dragons isn't a head-to-head competition, but it needs someone who is impartial yet involved in the game to guarantee that everyone at the table plays by the rules. As the player who creates the game world and adventures that take place within it, the DM is a natural fit to take on the referee role.
As a referee, the DM acts as a mediator between the rules and the players."
And now I'm pondering the choice of mediator. Can you have a mediator without two feuding parties (the rules and players) in this case? That seems odd.
In any case, it feels like page 5 should be read in light of what precedes it:
Pg. 4 - "And as a referee, the DM interprets the rules and decides when to abide by them and when to change them."
and, given a choice in how it is read, a reading which does not contradict what comes later would be preferred. In particular page 235 separates player and DM die rolling, and as others note allows fudging.