1. Are oscilloscope probe leads suitable for use with this unit?
The "B" input* has a 1 Mohm impedance and so a 'scope probe would be ideal to use here.
The "A" input* is 50ohm impedance. You could use a 1:1 probe, but a ÷10 probe would give a very high
attenuation. As long as the counter has enough input to count reliably, it does not matter.
I sometimes use a scope proble on my counter or spectrum analyser, when looking for a frequency, but if I want to make a measurement of voltage on the analyser, I use a coax cable.
* Another edit, I originally assumed that the A input was the low frequency high impedance input, but no, it is B on this counter.
My counter, a Racal, has the A input as the LF input.
Dont you just hate it when this sort of thing happens
2. If I make a DIY set of leads for measuring (and/or to connect to an oscilloscope), is it 'correct' to use 50 Ohm cable, and will it matter if the inner core of the cable is stranded or solid?
50ohm coax will do just fine, solid or stranded is OK.
However, you may find the coax a bit stiff, if you can find some thin flexible coax you will find it easier to use.
I have a few cables "BNC to Crocs" which I use for general test situations, I think they started life a BNC to BNC in some computer/communication/what have you system, nice flexible coax about 3mm diameter. I cut them up and fitted croc clips on the cut end, and was pleased with the result.
Lastly, I do not know when this Frequency Counter was last calibrated. As a guide, how regularly should it be serviced for novice use? I assume these units have been well built and are quite stable, yes?
For your application I dont think you need to worry about calibration.
HP equipment was very well made, if it works it is 99.9% sure to be OK.
JimB
Editing:
plus a BNC connector at rear to connect to an oscilloscope.
Just having had a look at the photo of the rear of the counter, the OSC connector is not for connection to an oscilloscope.
It is almost certainly an output from the frequency standard oscillator within the counter.