Brunni (./27) :
How does it show up on a 60 Hz TV then? I thought the signal (at least on the cable, not talking RGB, which I assume has various frequencies available like VGA) had to be the same as the TV, and coincidentally the mains network (AC)

The mains network frequency only mattered for very old TV sets (if the vertical refresh frequency was different from the mains frequency, you'd get interference on the screen). But it was not a deliberate design decision, only a side effect of the limitations of old electronics. In the 1980s, it was no longer a problem, so both frequencies could be different.

Brunni (./27) :
Basically is it the signal that drives the electron beam (meaning we could overclock and fry the TV), or is it the TV itself, which is fixed, and the signal should be at a certain speed, just like TV programs?

It's a little bit of both

Basic CRT TVs (especially in the USA) were only designed to work at a single vertical frequency. The TV itself has internal oscillators that generate the sweep signals for the electron beam. But it still needs horizontal and vertical synchronization pulses in the video signal, otherwise it wouldn't know when to do the retrace, and it would also drift out of sync with the video signal eventually (just like what happens with clocks).

The usual trick was to have the internal oscillators running a bit slower than the target frequencies, and reset it on each sync pulse from the video signal. That's why those TVs had a "vertical hold" setting to adjust the oscillator, and the picture would roll, look skewed diagonally, or completely scrambled if it was not set right (the same thing happens with consoles in RGB mode, if the RGB signals are connected but the sync signal isn't).

Since all of this was implemented with simple analog circuits, there were reasonable tolerances, so most CRT TVs would display a video signal correctly even if the frequency was not exactly right (and they also accepted non-standard sync signals to a degree, which plenty of early video games consoles took advantage of to make things simpler). More modern digital TVs are usually much less tolerant, and a lot more likely not to display correctly video signals that don't follow the standards.