I'm a contractor in Maine and we certainly have a lot of experience with ice dams. An ice dam can be the quickest way to force water under the roof shingles even on a roof in good shape.
I have had mixed results with heat tapes. When they are used properly, they can be somewhat effective. Most folks expect to see a nice bare zig zag pattern along the edge of the roof with the ice gone around the tape. Not how it works!
If you carefully read all the directions on many of the competing brand heat tapes out there, you will see that they do not claim to remove ice dams. They are designed only to create a small open tunnel under the ice dam to allow water that is trapped above the dam to drain off the roof. This is great in theory but here is where the reality sets in. If the tape does not extend slightly beyond or below the drip edge of the roof, it won't work. If the top edge of the tape does not extend above the ice dam, they will not work. If the gutters fill with ice and bridge the ice to the roof, they won't work.
Many of the tapes instruct you to only operate them when outdoor temps are 30 degrees and above. I have found that they are ineffective in temps much below 20 degrees. They also caution not to let them run continuously.
Running them in the bottom of a gutter is almost a complete waste of time and money. Since they only are capable of melting a small area around the tape, a gutter full of ice will stay full of ice! If the downspout is blocked with ice, forget it!
What I have also found is that folks get a false sense of security when they have them installed and neglect to remove the snow from the bottom 3 to 6 feet of their roofs, figuring the tape is a substitute for roof shoveling. Obviously, when they are installed, shoveling or using a roof rake gets a little tricky, so as not to rip the tape right off the roof.
I guess you can tell I am not a fan of these heat tapes. One method I have found to be extremely effective with dealing with an ice damn are nylon stockings or pantyhose (cut into two sections) filled with salt, calcium chloride or potassium chloride placed over the dam. They last several days and melt slowly and make a nice wide valley in the ice. I have seen hundreds of gallons of water pour off from behind an ice dam using them. Chopping the ice dam can damage the shingles and can be dangerous, but the filled stockings are fairly quick and easy.
If you have plants below or are concerned about salt staining your roof or siding etc, I highly recommend Potassium Chloride which will not harm plants, grass etc. You can usually find potassium chloride at your local hardware store.
I can't take credit for discovering this method, but thankfully I learned it from a tip on This Old House many years ago. I usually make up dozens of them in advance, so I am ready for all the calls from folks who wait too long and call to see if I can come fix the water leaking through their ceilings!
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
The building feature that you have indicated in your picture is designed in this case to provide an overhang over the front sidewalk. In this case the overhang provides cover during rainy conditions for persons coming to and leaving the business. Similar style overhangs such as this are also used for:
Often overhangs like this are built out from the face of the building and not tied into the original flat roof structure of the building. In these cases it is a lot easier to re-roof the original structure of the building and then separately address the roofing of the overhang unit and any flashing that deals with diverting water from the overhang onto the original roof.
In cases where an overhang like this is built up quite a bit higher than the original roof then it may be tied into framing that attaches into the original roof and cantilevers over the edge. This can make for a much more complex job in re-roofing the building.
As far as removal it will depend on a number of factors some of which include: