Dry walls nail pops and wall cracks in ceiling doors and windows
Nails popping up above the surface is a common event and usually isn't cause for alarm. The reason this occurs is from slight movement of the framing members (due to expansion and contraction) that over time works the nail loose. Conversely, if the pops and cracks have appeared in a relatively short period of time, it may be time to search more closely for a structural problem. Where I live earthquakes and tremors are common. This quickens the loosening of nails.
Your crawlspace and the framing lumber in it look to be in good shape. This is pretty rare for a house built in the 1940's. I would guess it had some work done not to long ago. If so there might be settling issues that are causing movement.
I can't offer an answer for the dripping noise from your duct/vents. If it is the sound of dripping water it would be wise to verify the problem and repair it soon.
Hammer the pops back in slightly below wall surface. Than screw a 1 5/8 inch drywall screw about 2 inches above the pop. Screws hold better. apply joint compound, let dry, sand, and paint.