A/C temperature control

The A/C temperature control in my 68 will not stay at the top / coldest position, as if a spring is pulling the lever back down (toward warm). Additionally, just turning on the fan switch (without selecting “max” or “fresh”) seems to engage the compressor. If I’m reading it correctly, the shop manual indicates the repair for the temperature lever to be an adjustment to the cable by moving it to within 1/8 inch of the full heat . Two questions - 1) Should that cable adjustment correct the temp control ? 2) What are possible causes for the compressor engaging just with turning on the fan switch?

Thanks in advance.