I'll do my best to help you out: when the guitar cable tip touches the floor while being plugged into the amp you get hum, I can't tell you exactly why (regarding the physics behind the whole thing) but that's just a natural thing that happens. Every guitar player has experienced this before.
The fact that the hum is diminished the moment you touch your strings has something to do with interference; your body actually produces a whole lot of EMI, again I can't actually explain why but as soon as you ground yourself via the bridge connection to your guitars output (by touching the grounded parts of your guitar) you have a path going from your body to earth: the noise goes away.
Of course the amp is gonna be dead silent as soon as you turn your volume knob to zero: you cut out the signal and every interference that gets in the way of the signal.
The tingling sensation is very probably current finding it's way through your body. As long as it's only tickling your fingers it's not dangerous, however it's a strong indicator that something is wrong with either your guitar wiring, your amp or the socket wiring in your house. If I was you I'd get my guitar checked by a tech, if the problems persist I'd either get a new amp or try out a different socket.
Hope someone else who's knowledgeable chimes in and contributes
Cheers
