Nails first because they readily conduct cold.
Nails from attic is normal.
Lumber used to build houses may contain moisture which is often absorbed from humidity in the.
Your contractor is correct in his interpretation of the national roofing contractors association standards as well as the ohio building code which state that nails must be long enough to penetrate through all roofing materials and extend through the underside of the deck or penetrate a wood plank by of an inch even if that surface is less than inch thick.
The nails sticking through the roof sheathing is normal.
You need much more ventilation in.
A point often overlooked is that since it s winter the water freezes on the cold nails.
As you age you may develop vertical ridges or your nails may be a bit more brittle.
You see this same thing happen in summer months when you place a glass of cold water or a can of cold soda or beer on an outdoor table.
Nail pops are largely due to wood or drywall movement and often appear within a year of construction.
The condensation is caused by warm air leaking through the insulation between the top floor and the attic.
The air in the attic has water in it and it condenses on the cold metal.
This is why you see the frost.
When you see water and ice on the nails the actual temperature of the nails is at or below the dew point of the air in the attic that is saturated with water vapor.
This exact same process is happening in your attic during extreme cold weather.
If the problem is the result of water or moisture penetrating the foundation or floor slab there are many remedial actions which may help.
The best solution for controlling moisture is at its source.
Hammer a new nail into the roof about 1 inch above the hole from the previous nail.
When nail pops show up on the ceiling of the floor just beneath the attic and near a wall intersection the culprit is a phenomenon known as truss uplift or a variation of it.
A moist attic means moist insulation and moist insulation is less effective.
Normal healthy nails appear smooth and have consistent coloring.