I agree, no less than 4/12 but the sheathing must be layered 100% with Ice & Water memebrane first.

The minimum pitch for an asphalt roof for Asphalt shingles is 2/12 or more as long as you use at least one layer of ice and water shield and one layer of synthethic felt under the architectural shingles.  I would never use a three tab shingle on this low pitch roof.   Below 2/12 pitch, I would use either an EDPM Membrane or the Resisto 2 0r 3 ply roll roofing membrane system.

Recommended not less than 4:12 pitch. Also would advise in Western NC to install ice & water guard in place of standard underlayment.

If you are asking about how to repair the roof damage, then I would like to suggest you to go for insurance claim process if you are already done with an insurance of roof damage. Because the plumber will cost you more, so you take some helpful hints from the Public adjusters about how to get the maximum claim amount on the Roof damage.

A good way to add value to your house is to do home improvement. Many renovation and home additions add value to the house. Also, painting by interior painting San Jose is a good way to add value to the house. One of the simplest and most cost-effective improvement is house painting. Low-maintenance landscaping also adds value when you sell your house.

Adding the stylish furniture in home can be very effective in increasing the home vlaue. 

The pictures were very helpful - thank you.  It looks like only the first ply/layer came apart which is not optimal but minimal risk for coming apart allowing the ridge vent to come off especially if they used every nail hole during installation. The bug barrier appears to be intact and the breakage of the plywood would not interfere with that.

Many pests like raccoons, squirrels or mice crawl into the house through the attic and crawl spaces if there are no barriers to prevent them from getting in. They may have mites, fleas, bugs and other pests, which may infest your home. Therefore it is necessary to implant a proper barrier and maintain a proper ventilation in our attics. The pest exterminator New Jersey professionals may also be consulted for the same to get better suggestions.

That would really be a question for the roofer on the split wood.  As for a bug barrier; that would be a question for a pest control company but that has never been a significant issue in our experience.  It is very important that there be adequate ventilation in all attic spaces that are not heated.

The new ridge vent should have the bug/snow/rain barrier integrated into the venting system. There are probably many other areas in the attic into which "bugs" could enter, but attics do not typically make the best habitats since the temperatures can be extreme and there is no "relatively nearby" source of water for them to survive. The "integrated mesh" is more for helping to prevent wind blown rain and snow from entering the attic space and settling on whatevr lies below.