Pump is a tiny motor that pushes on a diaphragm to move the coolant across microfins. If the motor is showing rpm, it's obviously working, the only way it'll not move coolant is if either the diaphragm is toast or there's a blockage to the coolant by air bubble or algae. You can try a light flick to the pump itself or even giving the pc (when it's unplugged) a shake.
The psu blew. Don't assume it's the aio, it could very well be working fine. It could be the cpu quite easily, or the sensor addressed by the cpu_fan header. When a cpu blows everything attached to it, gpu, cpu, motherboard, drives, ram, aio, everything becomes suspect.
Look in Cam, set the temp to respond to liquid, not cpu, after half an hour the coolant with a 90°C + cpu should be well into the 40's, closer to 50°C if it's moving, but takes that long to climatize. At that temp, the fans should have raised rpm significantly.
What would cause a Evga 850w G2 to blow? That psu has plenty of protective circuitry, and is very high quality build, blowing is not usually something they are known for, usually psus like that just roll over and die, if they die at all.