I've done it successfully with 2" of closed-cell polyurethane spray foam when there is not a serious water penetration problem and the stonework can be made clean and tight. The code required protection of the foam is not fire-rated; it is only a "thermal barrier" to avoid outgasing and smoke from the foam during a fire and is normally required to be 1/2" gypsum wall board. The use of intumescent paint must be shown to prevent the foam from reaching a certain temperature after 15 minutes of exposure to fire. Don't leave foam plastic insulation exposed; it's a killer. Since you are insulating the basement you obviously intend to use it so you need at least a 3" think concrete slab over a vapor retarder membrane. Insulation under it would be a bonus which is usually only required by code in multi-family dwellings. It's OK to lower the sub-surface as long as the bottom of the foundation wall and central piers are not undermined. If you have water infiltration issues use Worthy's link. The temperature of the earth outside may be increased a few degrees by the unheated uninsulated basement but the only part of the earth that must be protected from freezing is directly below the bottom of the foundation wall but the wall should be deep enough to be protected. Worthy is right about opinions.

Macbirch, we have a house with both. Half of it is slab and then there's a partial basement. FWIW, I can't really tell the difference in hardness between the slab and the basement halves. BUT there is a marked difference in floor temperature. The slab floor does have slab heat embedded which makes it quite toasty and comfortable but it also drives our electric bill into the stratosphere. What seems to be hardest on my feet is the tile flooring throughout the house. It really doesn't matter whether I'm on slab or wood subflooring. I'm looking to replace all of it with cork. I used to walk around barefoot. But my feet have deteriorated (aging is tough) - left foot has morton's neuroma (shoes are bad) and I broke the middle toe on my right foot shortly after moving in - on the @#$@ tile floor - and didn't heal right (barefoot is bad). In both cases, hard cold flooring is awful.

Tonight DH and I discussed how we want the contractor to finish the tub and walk in closet bumpout. And to what degree we want it completed. DH is an itch about doing things so-so, therefore it will be better to add the tiles ourselves, and do the painting as well. BUT, the electrical, the plumbing, the windows, the removal of the old pair of windows in the bedroom to allow entry into the new closet, that will be framed and cut by the contractor. Also, drywall and taped, but we will finish with a skim of plaster--or so DH thinks. I am ready to leave the closet drywall plain. I am fed UP with DUST. In the tub bumpout, I've decided I want it all beadboard...roof and walls. I think there is a synthetic beadboard mfg by a company with a name beginning with "A"...am I right? That would be very very water proof or moisture resistant. Of course the contractor will do the foundation, the framing, the roof as well. Our windows will be up high near the little rafter "tails" that stick out all around the house. The clerestory "lights" will be NON opening, and made of Lexan. DH says that if you make them less than 24 inches (they will be about 16) you do not have to allow for expansion/contraction of the Lexan. So each small panel can be caulked in and screwed down. That will give us natural light all along our northern exposure, and require no window treatments. I want these Lexan panels in the walkin closet also. I already have the wire closet kit to make high and low hanging racks and such.In fact, I might even get the contractor to install them for me. The top shelf rack will come about the height of the window bottoms. The roofline will just extend at its current angle, and we will lose a little closet height near the outer new wall...but not enough to create a problem. Having the "lights" up high will really take advantage of ambient natural light coming from the north, which is true and consistent all year long, winter and summer. For closet doors, I plan to get two pairs of bifold with frosted glass in the top panels, and louvered fixed shutters in the bottom panels. They can be installed later by us, because the brand I want is special order from Lowes. I also already have the tub fixtures/plumbing stuff ready to be installed. And the two short sconces and one longer double ended sconce for the sink, and the towel bars and racks and ONE grab bar. I plan on more of these grab bars, and will ask the contractor to place a lot of blocking in the walls while they are open. I am so excited. I've tried not to get my hopes up, this might not work out, but OH BOY I"M READY TO TAKE A TUB BATH. If the man is a professional, this job should not take very long, should it?

Were this mine, I'd consider building a dual purpose feature (fire pit/BBQ) since your foundation is already there. Choose the height of your raised fire brick burn pit carefully and, from the higher deck, it could be a fire pit but while you're standing on the lower deck, the added height would make it usable as a BBQ. You would, of course, need to remove the railings from around it. Edit: Or not. On a windy day, that could be dangerous.