Isn't there a can of freon made that can be bought by a regular Joe and is compatible with r12?
No! Theres no refrigerant that can be added to a system that already contains R12.
The low pressure cycling switch cuts the compressor off @ around 25psi to prevent the evaporator from freezing up. On a cool day it may cycle quite often, on a hot day it may never cycle off.
Also the fan speed has much to do with cycling. Low fan = more cycling and high fan speed = less cycling.
Last I heard, you don't need a license to buy it anymore.
You heard wrong. Nothing has changed and you still need a cert to buy it (legally).