insulated wire giving shock
If you get an electric shock when touching the plug of the extension lead then it is likely that the plug and/or the wiring inside is at fault. From the pictures you showed, I would suggest removing the old plug and replacing it with a good-quality new plug, also cutting back the wire to start in a new place.

A neon mains tester such as you showed in another picture works by you being a capacitor (this is normal, nothing to worry about). There is an explanation at How does the tester screwdriver work?

I notice that the extension cord is only two wires. A safer version would have two wires with another insulator over them, like this:



(Image from the CPC website)

However, what I recommend is to buy a new extension lead with a moulded-on plug and socket. This accomplishes two things: it will be safe, and it shows you care.