Jim, maybe someone else will be able to give you a "100%" yes or no answer to your qeestion, but I would say No it does not shut down automatically when it runs out of nails. I have numerous nailers and non of them do, so I add nails to the nailer in between the little "tasks" on the job.
Ray, I use a small "pancake" style for portability which came from the factory with a pressure setting of 80 # kick on and 105 to 110 psi kick off. When using the nailer with 1/2" to 1 1/4" inch nails it works good throughout the entire pressure range if the material is pine. If you plan on using longer nails or harder wood, I would make sure the pressure stays above 95#. Hope this helps.
No, this pneumatic pin nailer requires lubrication oil.
Even though in the description it does use the word cordless, which would make you think it works on batteries, it actually only works on your air compressor, see the first word of the description "Pneumatic"