(sorry for the wall of text!)
Brunni (./35) :
Got it 
thanks. So basically the beam scan mechanism has a fixed speed inside TVs, but it "waits" for the signal during synchronisation periods, which allows to effectively draw a little faster or a little slower if those sync signals come early/late?
No, the sweep rate is constant. So when the sync frequency is a bit higher than it should be, the picture displayed gets a bit smaller (and vice-versa).
Brunni (./35) :
[Edit] Or I am totally à la rue and there is no notion of pixel at all in an analog TV set?
Correct. There's no such thing as an analog pixel
One important thing to remember when thinking about traditional TV is that it's really old technology ; the development began roughly one century ago. The fundamental digital bricks we use today (ADCs, RAM, even basic things like counters) would have been too expensive to be used in consumer TV sets, too difficult to manufacture, or just not invented yet. And even analog components were costly and had limited precision (say ±10% at best, often ±20% or more) ; quartz crystals oscillators were only used by the military or laboratories. If you needed more precision, you had to tweak things manually with potentiometers, and hope that it wouldn't drift too much with time and temperature variations.
So traditional TV systems had to be designed to work without relying on precise numbers or timings, or complicated circuits (on the TV side, anyways). For people like us who were born in a digital world, it's a "paradigm shift" in reverse
By the way, this is also the reason why CRT TVs have overscan. As mentioned above, the picture size and centering can vary a bit depending on the video signal frequency ; but they're also influenced by other things, like the average brightness of what's displayed, and the mains voltage (not by design, but because of implementation limitations). If the TV was adjusted to make the picture fill the screen exactly in "average" conditions, then there would be situations where the picture would be a bit too small, or off-center, creating black borders around it. So instead, it's adjusted to make the picture slightly larger than the screen ; this creates a small amount of (variable) cropping instead, but this is less noticeable. This is also why you shouldn't put important stuff too close to the edges of the screen, as it may be partially cut off or even invisible depending on the TV. (On computer CRT screens, cropping is not acceptable, so they have stricter tolerances and are usually set up to have some amount of visible borders.)
And the reason analog TV doesn't have pixels is simple. When you take a black-and-white CRT TV and look what happens when it draws a line, everything is continuous: not just the video and sweep signals, but the phosphor layer as well (it's uniform, like a piece of blank paper). The whole notion of the picture being made of a finite number of small-sized elements simply doesn't apply. (For color CRTs, this is a bit less true, since there are RGB dots or stripes in the shadow mask. But those don't have a specific alignment with the video picture, and they only exist because that's the easiest technical way to implement color. The signals are still continuous, and it would work just the same if it was possible to have 3 uniform overlaid layers for R, G and B, for example.)
This is why video games consoles can have various horizontal resolutions and still display fine on any TV. The TV only cares about how long each video line lasts ; it doesn't know and doesn't care about the number of pixels there are, or if the signal is even divisible into pixels at all. The reason why there aren't too many different resolutions is because:
1) the resolution depends on the video clock frequency, and some frequencies are more common than others
2) there's often additional contraints, e.g. having an integral number of 8 pixels-wide tiles/characters per line, etc.
But you can totally use "weird" resolutions if you want. For example, the Jaguar uses a video clock frequency, and thus resolutions, that don't match any other machine.
Same thing for the color decoding (by the way, for NTSC and PAL, it's not really FM, but QAM): there's no sampling involved, it's implemented with continuous (analog) processes.
However, even if there is no "hard" limit like the number of pixels per line on an LCD screen, that doesn't mean that there's no limit, either. Finer details needs more bandwidth (higher frequencies), and analog monitors have a limited amount of bandwidth. Once you go over the bandwidth, the contrast goes down as the frequency rises, like taking a picture with a film camera that has cheap optics or is slightly out-of-focus: things that are too small are dim and fuzzy.
(There are also other factors, like the fact that the spot on the phosphor from the electron beam is not infinitely small.)
RGB, S-video, composite and RF are rated from sharpest to fuzziest in this order, because the video bandwidth of each format is lower than the one before. And colors look smeared on anything other than RGB, because the bandwidth for chroma is much lower than the bandwidth of luminance.
The limited amount of bandwidth means that there's no point in very high resolutions for retro home consoles: it requires faster chips, more RAM, etc. for a limited improvement. Especially since TVs outside of Europe typically had only composite inputs at best, or even just RF!
In the other direction (vertically), there's a countable number of video lines, but that's mostly because sync pulses are, well, pulses instead of continuous signals. Analog TVs don't really care about the number of lines ; as long as the timings are close enough, they will just draw fewer or more lines with no issue. (Some Atari 2600 games do this, and don't display right on digital TVs for this reason. But of course, when they were released, there were no digital TV on the market.). They don't even require the number of lines to be an integer ; you can put the vertical refresh pulse right in the middle of a line, and that's even exactly how interlacing is implemented.
thanks. So basically the beam scan mechanism has a fixed speed inside TVs, but it "waits" for the signal during synchronisation periods, which allows to effectively draw a little faster or a little slower if those sync signals come early/late? The pixel clock, however, is universal for a NTSC or PAL signal, right?