photography - What is the relationship between the focal length and f number of a telescope compared to a guide scope?

Don't worry about the main telescope. There doesn't have to be a relationship between the focal length and f ratio of the telescope and the guidescope. I think this is proven by the use of off-axis-guiders, which use the same focal length as the telescope. They just come with the headache of finding guide stars.

What is important is: can the guidescope provide data for the controlling software to accurately automate the telescope?

You want a wide, fast field of view, so that you are guaranteed to be able to find a bright star to guide by.

You want a camera on the guidescope that has sufficiently small pixels that the guide star that gets picked will at least cover a few pixels - the more the better. To some extent, this conflicts with the wish for a wide, fast view, as that will result in smaller stars on the sensor. This can be mitigated by ever so slightly de-focusing the guidescope so the stars form fuzzier, larger circles on the sensor.

What is more important that the focal length of your telescope will be: (a) what the limit of your seeing tends to be, and (b) the accuracy with which your mount can be controlled, and (c) how accurately the guiding software can place the guide star (usually a fraction of a pixel - use maybe 0.2 pixels as a worst case, if unknown).

There is not much point in being more accurate than the seeing permits.

The formula for figuring out how much each pixel sees is:
$$
px_{fov}=206*px_{microns} / f_l
$$
where f_l is the focal length of a telescope and px_microns is how large each pixel is on the sensor.

You can therefore estimate a suitable focal length guide scope this way:
$$
f_l = px_{microns} / (res_{seeing}/G_{acc}) * 206
$$
where px_microns is the size of the sensor pixels,

res_seeing is how accurate you need the guiding to be,

G_acc is the guider software's centroid accuracy (use 0.2 as a worst case if unknown)