Sure, the city might have noticed the stair error but they would have had no obligation to you to do so; they could have issued a permit and then flag it as a violation after it had been built, so never rely on an inspector for code compliance, that's your responsibility even if you hire a designer and a builder. Regarding the future room square footage, are you asking about zoning ordinance, building code, sewer/septic, or HOA regulations? I can't think of any maximum square footage restrictions in a building code; it is primarily concerned with safety and energy conservation so if you show a door to the space you must give it a use and design the floor structure for that use even if it is only storage. So call it storage so you don't need emergency escape windows and design the floor structure for a bedroom/living loading. You would probably show exterior insulation, a utility light, subflooring and omit all finishes. Are you suggesting that you might build above the Great Room later? Incidentally, a two-story space on a corner of a building needs additional attention for lateral bracing because wind forces are greater at corners and it is the floor that provides bracing for exterior walls so be sure to hire a good structural engineer.

If you have the capacity on the boiler I'd stick with hydro-air. However, nowhere do you mention AC in your post. I lived in MA for 25 yrs and you want de-humidification. I would suggest you look at a mini-split heat pump for your addition. Much easier to run small line sets rather than ductwork and the system will give you excellent heat as well as cooling. Mini-splits are very popular on the Cape. It is a fine place to live.

The practical definition of a Juliet balcony is a deck that doesn't have a platform, only guard railings. The code interpretation issue is whether or not the exception to R311.3 that allows a landing less than 36" in the direction of travel is satisfied with a dimension of 0". The next question is what dimension would be allowed (2", 4", 6" etc.) I suspect you will find that your contractor knows what he is talking about. You won't be the first person to ask the building department for an interpretation of the exception to R311.3 and you may be successful but the only thing that is certain is that they cannot refuse the 4x6 deck the contractor proposed and they might accept brackets down to the existing foundation that would avoid foundation piers. They might also accept a 3x3 deck. The biggest waste of money would be the construction of two foundation piers that would later be abandoned. Ask your contractor if brackets to the foundation would reduce the cost of a 4x6 deck. If so, that might be the best solution. The contractor's offer to install the ledger board is a sign of good faith. Make sure it is through-bolted and properly flashed according to the new more strict code requirements added to the IRC after so many fatal deck failures. I recommend Grace Vycor Plus under the building wrap and over the top of the pressure treated ledger board and that should be protected with metal flashing (no unfinished aluminum). Metal flashings do not weather well when in constant contact with water on top of a ledger board so the vycor will prevent water intrusion when the metal flashing inevitably fails. the metal is essentially protecting the Vycor from UV rays. I stopped using ledger boards 40 years ago even for decks close to the ground. I always use Maine Deck Brackets.

I installed a mini split in the upstairs of my 2000 sq ft home a few years ago. It is in a large open room used as the main bedroom. I seldom turn it on, as I like to sleep cold (but if the outside temps go into the 30's I'll use it to warm the room). We don't normally need air conditioning here (PNW) because the nights cool nicely, my room has walls of windows, so it sleeps like a screened porch almost. I live near the saltwater and benefit from cooling breezes after dark. My lower floor (the main living area), stays cool for the most part. But a few years ago, the forest fire smoke choked the air and I couldn't open the windows to cool the upstairs in the summer, and it was stifling. So, I put in the mini split but didn't really use it for air conditioning because the following year we had no smoke, so I just kept the windows open...until last year when we had a record breaking heat wave with temps near 110 or over. Even the normally cool downstairs got sweltering, the upstairs unbearable. The two floors are connected by a small entryway/stairwell with a door at the top of the stairs and door at in the entry leading to the living room, kitchen/dining, which makes keeping the heating zones easily separated. I keep the doors to the bedrooms on the main floor closed always But last year when it was so hot, I ran the air upstairs and opened the doors between the floors. The mini split kept the upstairs cool, kept the downstairs not so cool, but cooler than without. I finally remembered I have portable fans, so I set those up downstairs to move the air and make it feel cooler. This year, I added a mini split downstairs, just in case we have such suffocating heat in the future. I would not rely on the upstairs unit to cool the downstairs effectively, but it will likely provide some cooling as Elmer describes, when the hot air from downstairs rises and gets cooled. But it's not powerful enough to draw much air from downstairs via the fan system.