Those are very good questions - especially the use of screened cables is often dubious.
are PC and Switch properly connected with a shielded link betweend each other, effectively reducing EMI interference?
Yes and no.
Yes if the grounding on both sides is properly (=professionally) done and there is very little to no compensating current. No if there's a problem with grounding - in that case it's better to use unshielded cabling as badly grounded shielding increases noise. Note that Ethernet over twisted pair is generally free of potential and there no real need for electrical grounding. (Your local regulations might say otherwise, so do check them.)
is a connection like this secure?
Safe to handle? Yes, unless there's something really wrong with the electrical installation.
should had I connect the drain wire not to the metallic shield of the RJ45 plug but to the ground wire of my power grid (the yellow/green wire) even if the two devices are themself grounded?
The yellow/green wire is the protective conductor, not general ground. Of course, it's all wired together at the equalization point, but due to cable resistance and capacitance there may be residue voltage and noise. If you use it for grounding and introduce larger equalization currents you may quickly trip your RCD/GFCI.
The rule of thumb: only use shielded cables if you know your electrical installation provides good grounding. In any other case use unshielded cables.