Though you do not state it specifically, you appear to be considering sealing up the attic and foaming under the roof deck. The roofer that says that will reduce the life of the shingles is full of it, but most all of them say that. It might increase the temp of the shingles a little, but they are already hot and will not get that much hotter. I can not comment on the wisdom of sealing the attic in your climate. It is advised where it is hot and humid on the Gulf of Mexico coast. Sealing the attic would transform your attic from outside to inside and cut duct losses. In addition, it makes all those leaks between the living space and attic largely irrelevant, holes drilled for cables, can lights, etc. It could, however, cause moisture problems. You see, in my climate, the excess moisture is almost always outside. In the winter, where you live, it can be inside. Go to buildingscience.com and see what you can find about sealed attics in your climate. You are right to worry about your furnace. Unless it has its own air intake direct to the combustion chamber, you need to supply outside air if you seal the attic. Fortunately, there is an easy solution. An interlocked fresh air damper can be installed. These devices will not allow the furnace to start unless the damper is in the open position.

Obviously roof first and best in spring or fall (plus you don;t want the insulation and or HVAC to get wet. Then coordinate the insulation and HVAC depending on the necessary requirements of each contractor.

What did the inspector say about it? What type is it? How old? If the substrate is solid and there is not a bunch of moisture present. I would look into a SPF(foam) roof being applied. Look in the phone book and see if there are any roof contractors that specialise in foam roofing. I would contact them all and have them come out and give you a inspection and quote. With foam there is no tear off and the foam is seemless. They also put on a 30mil coating. Usually a acrylic, which can last 10 years. The cost is about $4 per sqft for 1.5 inches of 3 lb foam and 2 coats of 1 gal per sqft primer and a final coat of 1.5 gal per sqft top coat. Both BASF and Henry have excellent systems. Just be sure your contactor has experience and is accredited. Also your roof must be sound and free from trapped moisture. Foam is a great alternative because it is seamless and can be recoated and there are many foam roofs in commercial enviroments that are 30 and fourty years old. In fact the Lousiana Superdome was just fitted with a SPF roof after Katrina. I also have a SPF roof on my condo done this last October. I think it is a great alternative for flat roofs.

What millworkman said: support the roof with a post or jack or temporary wall, then cut the bad post out. Use a post base on the replacements. On the top part, I'd just take a sawzall and slice between the beam and the 2x6s to cut whatever fasteners are holding them together. There might be a bolt cast into the concrete that the post fits over, so slice the post in half a couple feet up, then pull off/out the pieces. Once you get one out you'll know what you've got to work with on the rest, and you can just lather, rinse, repeat.