Touching the heatsinks gives me a shock
I know that not grounding the supply is dangerous, but i do not come in contact with it nor will it run for a long time.
And it's obviously even more dangerous if you're getting a shock!!!! And, the intensity of the shock may depend on the conditions... what else you are touching and how the current flows through your body, etc. i.e., You might feel a slight shock when you touch something, but if you touch that same thing with one hand and ground with the other hand, the current-path is through your chest (and your heart). And if your body is wet/damp you'll get more current flow, etc.
When I was a "kid" my mother told me she was getting a tingle from her waffle iron. I was wearing sneakers and I didn't feel anything. I knew a little about electricity, so just to make sure I briefly reached-over and touched the water faucet at the same time... BLAM! Huge current through my chest. As you can tell it didn't kill me but we got rid of the waffle maker.
I've never seen a computer power supply that wasn't enclosed. You're probably not supposed to touch the heatsink!
1/ i measure 10 volts between my finger and the case/ the ground of the output. Does this mean that it is defect? If not, does it influence my circuit?
If the ground is truly earth-grounded, that's normal and safe. It's just your body acting like an antenna, picking-up electro-magnetic radiation from the power lines all-around you. If you've ver touched the input of an audio amplifier and heard a buzz, that's the 50/60Hz AC picked-up by your body. 10V is not dangerous, and you can't feel 10V.* If the ground is floating, who knows...
You usually CAN feel 60V, and anything over 50V is usually considered dangerous. 60V usually won't kill you, but there may be a higher-voltage peak/spike (with your meter showing the average) and we don't know where the voltage is coming from or if there is anything limiting it, and it may get worse (higher) under some different conditions.
2/ An opamp comparator followed by a transistor follower is connected to the output of the power supply (12volt), when measuring between the output of the follower and the ground of the power supply i measure +60 volts. How is this possible? Does it harm my components? But then when i connect the transistor follower to a resistor, then the voltage drops to 2/3 volt.. (supposed to be 10 volt). I do not understand what is happening here..
You'd have to show us a schematic. Maybe you've got a different ground/reference. i.e., It's possible to have 12V between the "red" and "black" power supply terminal also have 60V between the red-output and earth ground, if the black terminal is not earth-grounded.
Did you add the comparator & transistor, or is that built-into the switching supply? A comparator has a digital (all-or-nothing) output, so I'm not sure why you'd want a comparator on a power supply output, unless it's part of a switching supply/regulator. You're comparing what-to-what?
- You CAN feel the voltage from a 9V battery if you touch it to your tongue!