Macbook trackbar gives me electric shocks

Has anyone ever experienced a similar problem?

Have I? No.

Is my MB turning slowly into an explosive Galaxy Note 7?

No.

Is there any way I can contact Apple (English support and without requiring AppleCare plan) to help me solve this problem?

Although Apple insinuates that you need AppleCare for tech support this is untrue. Contact support and explain your issue. They will be more than happy to help.

Or, should I conclude that I am just screwed and, as my friends often joke, switch to a Dell XPS 13?

Apple should be able to help you with your issues.

And most importantly, what is the likelihood that this thing will one day decide to go ballistic and blast open my nuts?

Very unlikely. I would also not suggest eating nuts near your computer ;)

I just got my MacBook Pro 2 months ago. When I charge my Macbook, the top surface next to the mouse pad feels like it is vibrating and the edges give me a sudden shock.

This is what I did next: I attached a wire that is connected to the Earth terminal in the electrical wall socket and the other end to the Macbook Pro corner and viola, the vibration and shock disappeared.

The electric adaptor that converts AC 220V to 20/9 V DC into the USB Type C connector does not appear to be connected to the Earth terminal as you see below.