On second review of the photos, I don't think that the corrosion is due to electrolysis. The dielectric nipples should be adequate to prevent that and there is no sign of issues with the hot connection. As for the T&P connection, if the copper drain pipe does not come into contact with anything then there is no closed circuit for electrolysis to take place.
It looks more like corrosion due to a small leak over a long period of time. A leak that would not have always been noticeable, but would slowly get worse over time. You can see where the water has been dripping and there is signs of calcium buildup.
Like I mentioned in a previous comment, I would inspect the sacrificial anode rod and replace it if needed. As for the cold connection, you could:
- cut the copper line and unscrew the copper section from the nipple
- brush the nipple with a steel wire brush to remove the buildup
- reinstall the copper section using teflon tape and a joint compound on the nipple
- reconnect the copper line that you cut with a shark bite coupling or
a solder coupling if you know how
You could do the same with the T&P connection, just cut the vertical down pipe so that you can remove the copper pipe from the T&P and then remove the T&P, clean and reinstall.
You mentioned that the tank was installed in 2006, so it would be nearing the end of its life expectancy (most residential warranties are for 5 to 6 years) so I would keep an eye on the tank for any leaks.
In case you haven't noticed, weather varies ;) This alone could account for the different effects each winter. But I think you're right, other factors are at play here.
Ventilation. Your gross vent area is 1/100 the attic area, accounting for louvers, let's say about 1/150th of attic area. If you do not consider the gable ends as cross ventilated, it is barely adequate. But as a cross ventilated arrangement, it is more than adequate. Will more help? Yes. Will it be effective? Harder to say. More on this later.
Moisture. Frost on nails alone is not necessarily cause for alarm. Black mold growing where the ventilation is less effective is definitely cause for concern. I'm no mold expert, but you should at least spray some moldicide on it while you devise a more permanent solution. Since the attic is always warmer than outside air, for there to be enough moisture to condense in the attic, the moisture had to come from either inside the house or from a roof or plumbing leak. Running a humidifier frequently would significantly contribute to the amount of moisture migrating into the attic. You don't mention anything about a vapor barrier, you quite likely do not know.The amount of moisture you observe tells me you don't have an effective moisture or vapor barrier. Not only can this cause mold, but it will also diminish the effectiveness of the insulation.
Why frost on only one side? Most likely solar access. The nails are colder on one side because the roof angles are different. This has significant effect on roof surface temperature, even under a good layer of snow.
Not only can vapor migrate through the ceiling, it can be carried in through air leaking around openings in the ceiling, in particular the pull down steps. If the perimeter is not weatherstripped, much moisture (and heat!) can escape this way.
What to do. Your primary focus should be to limit moisture migration into the attic. This will not only solve the condensation problem, but also limit heat loss. Seal all ceiling penetrations. Not only the steps, but plumbing and electrical penetrations as well. Apply an effective vapor barrier. This is not easy. You don't mention your ceiling finishes, this can make it easy or difficult or expensive. You could simply sandwich plastic between the current ceiling and a thin new ceiling finish. If you have an expensive existing finish, you may need to pull up the attic insulation and spray a barrier down on the back surface.
Note that if your household generates a lot of moisture, a good vapor barrier could cause you to have problems with condensation in your ceiling finish. The only solution to this is reduce moisture generation and increase whole house ventilation, ideally through a heat exchanger of some sort.
Once you've reduced the moisture migration, you may not have a mold problem in the attic any more. You may not need any more ventilation at all. The areas near the eaves obviously are not well ventilated, so the addition of soffit vents is the best approach if more is needed. You will need to drill many holes in the separation board to gain free communication with added vents.
If that works out to be too much effort, adding ventilation elsewhere can still benefit the lower areas, though not as well as soffit vents. Anything that increases ventilation will help. More static vents, power vents, ridge vents, turbine vents, they all have their own pros and cons, but they will all increase ventilation. You can do just one measure or a combination of measures. There is no right solution, but there is something that will make more sense than the other options.
Best Answer
I wanted to comment on this but don't have enough reputation.
My childhood house had these marks in the basement on interior walls. They looked just like the marks in your picture. They only occurred on walls near my bathroom where people generally took long, hot showers.
I'm not saying this is the cause, but for me they clearly had a correlation with the steam from the shower. The more long and hot showers were taken the more visible the marks seemed to be.
Again, not really intending this as a good answer, but I cannot comment.