When twisting two cables (imagine f.e. something like a twisted pair cable), does the rotation of both cables have any importance? I.e., is it important that each cable rotates around its own axis as both cables are twisted together, or should it be kept "unrotated" so to be sure that possible side effects happen/don't happen?
The rotation of each cable around its center axis is unimportant electrically, though if it's extreme it could be important mechanically.
The reasons for twisting conductors together are to minimize inductance and to reject common-mode noise in differential applications (Noise incident on both cables is rejected by a differential receiver.) . In either case the important thing is the twist of the two conductors, not the twist of each individual cable in the pair.
I suggest you try twisting two thin cables together without individually rotating them. They will not stay twisted unless you individually rotate them in which case they will come together as a single twisted entity pretty much by themselves. It's the basic mechanism for making ropes from strands.
It's not really optional.
The important part is to have an uniform and symmetrical twist between the two wires of a pair for the pair to be useful.
It keeps the inductance and capacitance per unit length constant, which means it acts as a transmission line with certain impedance.
It also keeps the wire lengths equal, which means there will be not much intra-pair signal skew.
Twist rotation is less important for copper cables than it is for steel or fiber ropes, because copper has a smaller elastic range. But even copper has some elasticity: if you rotate correctly the residual springiness of the cables clamps the twist together.
If you don't rotate, or rotate incorrectly, you're adding additional work hardening to the wires. Hardening may be good or bad: unhardened pure copper is too soft to use for suspended cables, and the development of telegraph and telephone waited upon the development of suitable copper alloys and drawing technology.
It's all about common mode rejection and perfect matching of wire lengths and surface area as well as variation in insulation gap between conductors..
All power transmission lines are twisted by rotating sequential pairs every 1 km spacing. (You will notice this in highways.) This is to reduce the common mode magnetosphere injection of wobble in the magnetosphere from inducing high voltages in the grid at relatively low frequencies called Schumann resonances. They are triggered by Solar Flares like a guitar string. The worst case incident recorded was in the late 1800's called a Carrington Effect
Search: magnetosphere for references
But signals in twisted pairs often involve frequencies with skin effects so the exposure of insulated twist surfaces must be equal by the ratio , Area/length=k to achieve a common mode rejection ratio of k*20 log (k). As you might imagine, this coupling to free space and earth conductors or noise generating conductors nearby. The effect is bidirectional. The effect is rarely better than 60 dB.
A convenient way to achieve this is to put the wires in an electric drill chuck and while stretching them achieve 8 twists per foot.. This also adds about increases the differential capacitance from about 3"/pF to 1.2"/pF if I recall.. This provides some common mode rejection up to the microwave frequencies but will have a dependence on the common mode impedance to differential mode impedance ratio. So 50 ohm lines will perform better than high impedance pairs.
The individual wires in a cable are usually made of many strands twisted together.
The strands are to make the wires less stiff and the whole cable more flexible.
In the process of twisting these wires into a cable you can untwist the strands of the wire and modify the mechanical property of the whole cable - in my experience if you add extra twist (ie by coiling a cable incorrectly) it tends to kink.
If the cable kinks, then there can be extra space between wires and this modifies the wire to wire capacitance and a kinked loop can add inductance.