the uk? wit de funny fuses in the plugs?
the C3 addition is simply good practice, in any supply. it provides a "local bucket" as the experts call it, from which the circuit can get juice when it needs, and it also provides a low-impedance, smoothing path to ground for all the hash and noise long cables like to pick up.
from what I can see, without having built this myself, the D1 provides a bypass to the resistor in one direction only, so the resistor will allow a slow charge, but a fast discharge (I don't have the circuit in front me the moment, so this may be the other way round).
as for the relay, and as I keep hinting at, if it is wired as circuit-drawn, the switch contacts-ing has no common to the power section, so there should be no way the relay contacts can contribute hum. if the relay is chattering, it might make a hell of a noise, but it isn't, is it? and if there was a load of digital junk in the amp, the leads might pick it up, but there isn't any. with the gt8 in the next room, all the digital hash its internals will and do generate are too far away, and not connected anyway.
turning down the guit killing the noise may very well be a pointer to the rooot cause, but I'm not smart enough to know what that might be. so, all I can suggest is doing a nice tidy re-wire, so we can look in and say "yes, it's all wired as per the diagram". and then, if it still makes the noise, probably start a new thread, with a new title, to draw in some of the more knowledgable types. we'll get there in the end.