Power vibrations through laptop, over whole body...?!

This "fuzzy" feeling happens indeed because Apple's chargers aren't grounded/earthed. It will go away completely if you use a Power Adapter Extension Cable with your charger, available in the official Apple Store.

It's safe, it's a very small voltage, it's below the strict safety standards that governments set. Our skin is just pretty sensitive to it.

A portable Mac's case itself is not grounded (earthed) nor is there any regulatory requirement for it to be. The reason you perceive that sensation is that the enclosure is capacitively coupled to ground. The capacitance is such that it is impossible for it to carry sufficient current to pose any harm, but it is far more noticeable with 240V electrical systems than it is with 120V systems such as in the United States. When you touch the Mac you become part of that circuit. Think of it as becoming one with your Mac.

That design aspect is quite common among electronic devices. It makes electromagnetic interference with other devices less likely—which is a regulatory requirement.

Just make sure your Mac's power adapters are genuine Apple devices. Counterfeit devices are very common and very dangerous. If you have the slightest doubt follow BobTheFisherman's advice and bring your Mac and its power adapters to Apple to be evaluated for safety and authenticity.

Yes using a grounded plug can be a workaround. But it could be that your building wiring is not correctly grounded (earthed). Take your computer to an authorized service center for evaluation to eliminate that your computer is causing the issue.

Should i be worried that with too much usage, my girlfriend will turn into some kind of X-Man?

That's far more likely to happen to you, but only after you get married.