Thank you both for your tips and hints.
My current assumption goes with "old graphics cards", above I mistakenly called them "screen drivers". In fact, I used the NVidia Quadro 2200 with a modern driver for the Quadro 4000. I admit I only had the graphics card idea after posting here, so my edit above.
I should have been more specific, the thing I've observed on two completely different systems (on the second system I even had not installed most of my FF add-ons yet, but Addblock Plus, Click&Clean, and perhaps New Tab Override, I don't remember, so there is a chance the culprit is among those.
Next time I'll install it into a new system, I'll leave out those add-ins for some days, to check - it's only now that I see that with those add-ons, my FF was not a fresh installation, too bad.
It has nothing, or very little, to do with FF system load, on the other system it occurred almost instantly. It always (in both systems) comes with some sort of a shadow in the "menu" corner (top left corner) of FF, in other words, from that shadow, I can even see my input will not be processed if I try (on condition that I see that shadow first of course, but it's always there before, and it has nothing to do with the keyboard?).
This brings me to the fact that mouse and keyboard/keyboard driver were the same, too, so that is another possibility indeed, my saying "totally nother system" was wrong, obviously, so there's lots of possible reasons I realize now.
So I've disabled the "Filterkey" function, never knew what it was good for anyway, never used it in any way but it was on indeed. CPUBalance seems interesting, but does not work with XP. Have installed Cyberfox, will try it, first without add-ons, than with the more important ones, then with the rest of them, but the question remains, if Cyberfox was FF but without the memory problems, why doesn't everybody use Cyberfox? Correction: Cyberfox 52 is incompatible with XP, 45 seems to be compatible, in-between: doubtful. Will report my FF trial, as well as the CPUBalance trial, to after having bought a new pc.
For the "old graphics cards" and old computers. I have sent back the second-hand pc, for probable motherboard problems, should buy instead a modern and new i7 (6700 or 7700 or probably 6700 if I can it for less because of the 7700 being new now, I'm looking for sales) instead.
It was an i5, and it was far from running at the speed I had expected, ditto for the 4 gb graphics card: ridiculous! So it seems that when buying something new today, i5 is not good, let alone i3.
Also, 8GB of memory will suffice for most uses it seems, with that 16 GB thing I often checked the memory load, it it was never higher than 35, 40 p.c., while at the same time, as said, speed was much too low for my wishes. In other words, you'll need 16 MB when you run several heavy programs concurrently, but if not, you don't need them, and above all, plenty of memory will not replace processor power. (This may be an evidence, but it was good to have seen my own eyes.)
Old graphics cards are not good either: Office 2016 was preinstalled, but the graphics card, even with its modern driver - or because of the combination old card-new driver, but the old driver would not have been compatible with Windows 10 anyway -, did not correctly display the very last line in these Office applications: you typed without seeing what you typed.
So with your old pc, you know exactly what to expect from it, but with a new one, if it's a i3/i5, you risk to be quite let down; I would not have expected an i5 to be that lame, with quite simple (office) software - not speaking of video cut or such things.
But my problem with FF does not seem to be that widespread, so I'll have to check any "old" component with a new computer, incl. keyboard drivers etc.
This last element is probably even the one, since on forums, people complain about incompatibilities between Cherry kb drivers and newer Windows versions, and I had said on that other system the problem occurred five times as much as on my old one. And then, this does never occur in any other program than FF...