does the air condition fan cycle
If you have automatic climate control the fan may vary speed.
but does the fan cycle, by turning on and off , or does the speed vary
I don't know, you tell me what is does.
On most vehicles when the A/C compressor turns on the A/C cooling fans also turns on if your vehicle has a separate fan just for the A/C, so when the compressor cycles the fan will also cycle. Now there are some systems that use a high pressure switch that turn on the fan when the A/C systems high pressure reaches a preset point, however your Nissan is not one of those units. HTH
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