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I'm about to perform a few electrical changes in my house in order to be able to control lighting fixtures (230V, 30 to 200 mA) from a PC. I have a doubt about the way stranded wires should be connected to the plugs.

For instance, I suppose the way of connecting the wires shown on the next photo is dangerous, because the connection can easily become loose, is it? It seems that pulling the plug a few times by the wire instead of the plug itself would have disastrous effects on the connection.

If yes, should I solder stranded wire to make it solid? If so, what should I take care of, aside using a rosin-core solder? Once I solder it, how am I supposed to connect it to the metallic parts of the plug?

It's a given that any wires in cordage will be stranded. Being designed for a different kind of service is what makes cordage different from in-wall wiring, and why you should not use one for the other.

So it's a given that any plug whose primary use is cordage is designed to work with stranded wire. Here, you should follow the instructions and labeling on the plugs, because following those instructions are the basis for the testing and certification which the plug received from your NRTL. (Nationally Recognized Testing Laboratory).

Not following the instructions is an "off-label use" (to put it kindly) and can result in an illegal install and non-payout of fire insurance.

Speaking of non-payout, you need to be careful what you are sticking on mains power, and in particular, built into walls. Random electronic components out of the Digi-Key catalog are unfit for use in mains power. If they have a cert/listing from an NRTL, they may be fit for use as a component of equipment which is subsequently (as an assembly) certified/listed.

If your aim is smart appliance control, you may be better off using existing, listed/certified smart devices (i.e. Not Sonoff), and having your electronics communicate with them. Generally, the rules are greatly relaxed for homebrew equipment when it is entirely low voltage and fed by a listed/certified wall wart.

I would not use solder - it won't help the grip much (arguably, stranded wire may actually grip the screw better as it deforms) and while it is probably not a bad conductor, it won't beat copper.

What is important is to wind the wire around the screws in the correct direction. To quote Harper from another answer (and I have seen him mention this quite a few times): Hook the wire clockwise around the screw, so tightening the screw makes it wrap more.

One should never apply lead alloy solder to stranded wires (often called "tinning") that are to be tightened under a screw. Eventually, the solder will cold-flow under the pressure and the screw connection will become loose.

This doesn't happen overnight; it can take months or years. I have personally seen this happen on several occasions.

It can be okay to just tin the very tip, to help keep the twisted wire strands together while tightening the screw. However, it is preferable just to leave some extra wire sticking out, and cut that off flush after tightening the screw.

Generally speaking, no. The screws are designed to hold the wires in place.

If you don't feel the plug screws are sufficient, buy a newer one. They all use screws to connect, however.