Viktor,
You have two problems, the background hum and the crackling noise.
There are a number of things that can cause hum. A ground that is not well soldered becomes an "Ohmic" connection. That can be checked by touching up all the ground connections.
Another thing that might cause the background hum is the AC heaters to the tubes. They should be twisted well and flat against the top plate. The heater wires should be routed so they cross the signal wires at a 90 degree angle.
A loose ground or signal wire in your interconnects can cause hum... see the list goes on. Have you checked with the inputs grounded? (I think, can't remember all the posts in this thread, I think that your hum doesn't go away when the volume is all the way down. That eliminates anything upstream of the volume control.)
The noise might be the tube, swapping it for another, one at a time, can eliminate that. You will most likely roll tubes soon anyway so check the "Tube Rolling w/Crack" thread. It is always good to eliminate the tubes as the source of a problem.