[dcwired]

1/0 ground is big enough for a 400 amp service.
You can drill a hole in the outside panel at the bottom appropriate size, probably for a 3/4" connector (1 1/8" diameter).

 

[dcwired]

I cannot speak for your POCO or city, but I say the GEC goes on the main breaker section and, yes, it goes with the neutral which all of the lugs other than on the breakers are connected.