There is (or was) actually a magazine devoted to these issues...Natural Home (now Mother Earth Living). We have done a couple of houses for environmentally allergic clients. To address your questions one by one is difficult....but not impossible.

Fiberglass insulation is used on the outside of ducting, the old fiberglass interior insulation duct has been mothballed. Formaldehyde has been discontinued in plywood production and is illegal in California and the rest of the country is following suit. This applies to flooring and underlayment as well. Alternatives for cabinets include wheat board and soy glued products. Structural materials can be solid wood in some areas (not in earthquake country).
Natural wool carpet is usually OK in area rugs...testing of all materials is important. Closing in walls of attics and other bonus spaces will keep them clean, though the dirt does not come from the attic space itself. The dirt is a byproduct of convection or gravity venting, bringing outside air into the attic to keep the roof cold (tech stuff). Low VOC paints and finishes are readily available. Mystic Paints and Aura from Benjamin Moore come immediately to mind. Conversion varnish or lacquer on cabinets cures incredibly quickly. A day is all it takes...once again, testing is important. Wood treated with pesticides is for exterior applications. Redwood is an acceptable substitute as is cedar. Mudsills and wood that is in contact with dirt are generally pressure treated. The issue with pressure treated wood has been it's toxicity. New formulas that are non-toxic have been developed and are now in use. A mandatory measure from the EPA to reduce heavy metal poisoning. Insulation is available made from recycled and virgin cotton denim. Insulating foam from soy is also available and is non-toxic and worked for one of our jobs. Industrial sizing will not clean the HVAC system...electronic HEPA filters will and are readily available as an upgrade from your heating and cooling contractor. They filter particulates out to 3 microns. Wood flooring needs to be finished. A natural wood with a wax finish or an oil finish with wax topcoat is a natural material alternative. Marmoleum is a linseed oil and sawdust material with a jute fiber backing for kitchen and bath floors, like old time linoleum. Tile and grout are also quite safe to install.

So really..you are not trailblazing....this has all been done before. Finding a local professional is more of a challenge. We have gone much further than you are even contemplating to insure our clients health. Consider cast iron pipes instead of ABS plastic for drains, waste and venting. Copper with lead free solder (mandatory anyway) for all supplies. One issue that we had a difficult time with was caulking. Making it "natural" made it not work. We need caulking to seal a modern house. Our best results came with polyurethane caulk that was allowed to off gas for a month prior to close in.

I hope this helps...do try Mother Earth Living magazine for local resources and assistance.