In a word...NO. If a worker get's hurt, or your neighbors property is damaged they will most likely sue you. Your homeowners insurance policy will not cover you if your contractor is uninsured or if a permit is not pulled. Fraudulent contractors will often tell you that your homeowners policy will cover you and that they can save you money...they can cost you your home.
Tell them to stop! Properly installed siding will be nailed in firmly but with space for the shingles to expand and contract as per temperature variations. In the winter it will contract, in the summer it will expand. If they are nailed in too tightly or too loosely they will probably warp and it will look terrible. Not to mention that it can allow for water to damage your interior.
At this point, your best bet is probably to cut your losses and get a new contractor.
In some jurisdictions it is legal, however, you are putting 0ver 7,000 pounds of extra weight on your roof. That can do serious damage to the roof's framing especially when
you consider that each inch of snow weighs 1 pound per square foot. That means that a snow storm with 1 foot of snow weighs approximately 24,000 pounds. That kind of weight can cause serious damage.
Most happily married men know that usually, their wives are right...you certainly are!...lol. It does make a big difference....044 gauge material is considerably stronger and much more likely to survive a baseball hitting it or a branch crashing into it during a thunderstorm. 3/8 inch insulation behind it not only keeps your home warmer in the winter, but it strengthens the shingles themselves making cracks much less likely. Remind him that cutting corners almost always costs you more in the long run and that a husband who has a happy wife, has a happy life...
Sort of...it's true that you can't really tell the extent of framing damage to a roof until the old roof is torn off. However, a reputable company will tell you how much it will cost to replace each piece of sheathing and each rafter. This way, if you need 3 sheathing planks and 4 rafters, you'll know how much the cost should be...also, make sure they provide good pictures.