Very old Coldspot frig. - apparently made by Whirlpool
Problem - wires burnt off at compressor relay
Compressor checks ok w/ meter

the 3 existing parts are:
relay - FSP part no. 548834 or 9660-093-163 X2C
plate clock - FSP part no. 518842 or 3ARG1L4
Mallory capacitor - FSP part no. 531129 or 88-108 MFD

Appliance Pro shows relay/ overload replacement kit AP 3120015
Plate clock AP 2604723
capacitor AP3121743

Questions:

Are these the correct parts, or does the overload/relay kit replace more than one item?

Specifically, do I need the plate clock?

If these questions aren't helpful or cloud the issue, please disregard. The bottom line is I need to replace everything between the compressor and the incoming electric power whether it is part for part the same as it was, or whether there is a modern day replacement for the old system.

Please advise what to purchase.

Thank you.

I would first measure the resistance of the compressor windings with a digital meter. The top pin is usually common, the bottom left the start pin, bottom right, run. If you measure more ohms between the common and left bottom pin compared to the common and right bottom pin, you have the standard pinout.These older compressors always had a higher resistance start winding.
Usually, the start capacitor is oil filled and ok, then just order a URO41 (AP4503418) start relay, for 1/4 - 1/3 hp compressors about 3-4 amp running current. This item comes with wireing info and just plugs in.
If your capacitor is bad, you will have to order it from the values on it, like 45 u farad, 230 volts etc..
It is worth noting that many times the wires burnt because the compressor was drawing high current either from a power surge shorting the windings, or the burnt wires causing compressor stall and burnout. However it's worth a try to fix it. Also, your old freezer sucks about twice as much power compared to the new ones.

Resistance measurements will not determine if the compressor is good or not. Can only be verified when the run current is measured after the new start device is installed, keep us informed.