To me, the "buzz" , if it is power line frequency ( 60Hz in North America) , would make it appear like you have a ground loop. Two pieces of equipment that have grounded power cords, and are pluged into different outlets, or through various "power bars", etc, may end up creating a long enough connection betweem the chassis of each piece of gear that there is a slight differnce in what each "sees" as ground. This can cause enough current flowing along the ground of the interconnect cable to become part of the audio. Then you get hum.
In you case, removing the one piece of gear from the chain ( the mixer ) stops the hum, so either the amp or the mixer could be the problem. If everything else can be connected to the amp, and no hum, then blame the mixer, if the othe way around, blame the amp. Note that even when turned "off" the chassis will still be grounded anyways, so being turned off will not stop a ground loop.
Here is a link to ground loops:
https://www.soundonsound.com/sos/1994_articles/aug94/groundloops.html
The hiss could be digital noise generated by some of the input control / switching logic. It could also be self generated by the amp oscillating or having a noisy pre-amp circuit.
If it is digital noise, some bypass caps at each of the IC's DC power terminals may cure that for you. If it's in the power/pre-amp it may be due to its design or choice of components, and harder to fix.