Need to determine the correct start capacitor for hvac unit
You have a single start cap there not a dual (from the wires I can see)  The resistor is a safety bleed down for the cap.  I would ASSUME that the blower motor uses a run cap and if you look on the upper right of the label on the blower motor it does give a run cap value of 5.5mfd.  Bleed resistors are not normal on run caps.  You may be able to find the value of the needed start cap by looking at the compressor nameplate.  You can use any cap of the correct capacitance and voltage and if it lacks a bleed resistor and the bleed resistor is still good on that cap in the picture you can move it to the new cap.  I'm sorry to tell you but none of your pictures have legible writing when blown up enough to read.