Thanks for the report Adam.
And yes, Flitz is recommended for the brass. Normally you use a brash polisher like Flitz on nonplated surfaces, but in this case, I'm thinking I would sand down the tailpiece and truss rod cover and then polish them with Flitz. The better fix would be to have them replated; but I have no idea how much that would cost.
I don't see anything suggesting the jack was replaced. It looks to me like someone stepped on a guitar cord that was still plugged into the jack and that the resulting pressure stressed the wood around the jack. But I'm just guessing.
The Comfort tapers on standard Essence fours and fives are:
4 string: Nut width 1.625; 24th fret width 2.360
5 string: Nut width 1.875; 24th fret width 2.930