A light-hearted explanation in response to DaveWalker5

True, but a single shot waveform time duration is measured in TIME

I thought the inverse of time was frequency , so it must have a frequency

It might be more correct to say that, "the inverse of the dimension of time is the dimension of frequency".

It takes me half an hour to get to work, but the frequency of my going to work is not twice an hour or 24 times a day.

My frequency of going to work is 5x a week or 1x a day (which of course look like different frequencies), but my time at work is not a fifth of a week, nor 1/1 day.

Frequency has the dimension "per second" but that is not its full title! Before they decided honour Heinrich we called it "cycles per second" and since "cycles" is a dimensionless number it does not appear in the unit dimensions.

A single shot event is not cyclical and does not have a frequency. If there were a cycle - say, you trigger the event, make some measurements, jot them down, then try again - then the time for that cycle would be the inverse of the frequency of your running the test.

I have been trying to think of another unit like this, but the only ones I could find are the Bequerel which is also "per second" and wave number which is "per metre" -neither of which seems helpful to the intuitive understanding of this idea.

You are however in good company in making this leap of imagination. In digital signal processing one has to take a finite sample of a signal, which is not even going to be an exact multiple of cycles of any cyclic content. Mathematically you imagine that this sample is repeated infinitely in both senses of time and when this is processed, not surprisingly you find frequencies which are not really there and you distort the relative amounts of those that are there. But underlying all that jiggery-pokery is the assumption that a single finite sample, such as you get from a one-shot event, COULD represent a meaningful slice out of an infinite repeating signal.

Also, if you fed your one-shot square pulse signal into a spectrum analyser, the biggest peak would be the frequency corresponding to to the reciprocal of twice the duration of the pulse. (Maybe the second biggest peak, if you include zero frequency? I'm not sure how real spectrum analysers handle this.)

All that aside, You are, as people have said, much better off measuring the time for slow signals and calculating a frequency if this is appropriate.

As for the 5V into 50 Ohm, 10V into 75 Ohm, etc, I'm as mystified as you. I can see the need for a MINIMUM signal to ensure accurate triggering. But the only reason I can see for a MAXIMUM signal, is to protect the components (mainly semiconductors from excess voltage and resistors from excess current.) In which case the answer would be, if you exceed these the circuit will be damaged and simply not work any more!

In many situations an excessive input will cause distortion of the waveform, but for a counter, as far as I understand it, all that matters is the the zero crossings of the signal. Typical compression caused by overload would not affect this, I think.