Does the computer really shut down after I shut it down

After I pressed Start >> Shut Down >> U, the computer goes off. But hass the power supply still got energy?

When I use my old power supply, after I shut down the computer, the light of my mouse is still on, indicating the motherboard still has energy connected to the mouse.

However, after I switched to a new power supply, and after I shut down the computer, the light on the mouse is off. So is this event controlled by the power supply?

What I concern is whether there is still wasting energy after I shut down the pc.

Secondly, if it is on, how much energy it is eating? Full power of the power supply?

And more importantly, I would like to state why I don't want to unplug my computer.

Here is the case:

I got a wall and a socket hole, and the socket is connected to a 6-sockets power strip. The power strip is plugged with many thing, most are computer accessories. One day I want to shut down the computer completely, so I turn off the switch on the socket which connected to my pc. It is fine for the day. And after a few times of this action, one time, after I switched off the socket, my house's electricity is all gone and I found out that there must be leaked electricity so that Leakage circuit breaker shut down the electricity supply of my house. I need to call the administrator of the building to release the electricity from outside of my house. And this event deformed the socket on the power strip which connected to the pc, no matter whether I turned on/off the switch, there is power in it, so I think its circuit was melt so that the switch cannot control it anymore.

After this, I checked many suspects for this event, the socket on the wall, it is replaced with a new one. The Leakage circuit breaker is fine(checked by professional guy). The power strip is replaced with a new one. Then I turn on my pc with the switch.(I don't remembered whether that is a turn-on or a turn off) Hell, all of the electricity was gone again, and the new power strip was deformed just like the previous one.

Then I replaced my old power supply, the brand of it is GTR, which infamous among computer users who says the power supply from brand GTR will make fireworks and is very dangerous.

Then I got a new supply, and now I've never try to turn off the computer by turning off the switch on the power strip. Too dangerous.

Now I remembered I've never turned off the switch on the back of the power supply before turning off the switch on the power strip. Do I needed to turn it off before? I need to be educated about this whole proper procedure to shut down a pc completely.