The best performing, for low temp and otherwise, mini-splits are the 1:1 models. I believe that the better match between indoor and outdoor unit capacity is what does it. I can't, unfortunately, comment personally on their performance at temps that low. Where are you going to run the lines up to the second floor, on the outside of the building? If so, do you have a good way to hide them? (I have a single-story installation on a raised home and mine go through the interior walls.) Why Mitsubishi, Sanyo and Toshiba might offer more versatile remotes or different types of indoor units that fit your needs better. Mitsubishi does not offer electric resistance back up heat for when they are defrosting. IIRC, others do. Please do look into alternatives to the most common wall-mounted units.

Base cabinets should be installed at the same level as the finished floor. Usually this means the finish floor runs under the base cabinets. The only time you CAN"T install base cabinets on top of the finish floor is with a floating floor. In this case, the flooring must be removed (or not installed) in the area of the cabinet footprint. The correct way to raise the subfloor to the same level as the finish floor is to install plywood or cement board underlayment under the cabinet footprint. Because the flooring in never completely level, base cabinets usually have shims underneath at least one or two corners. Sometimes they are shimmed all around. Shims are part of a cabinet installation, the use of shims is not a problem by itself. A stack of shims is not acceptable. They may not stay a stack. I use a single shim. If two shims are necessary, some adhesive needs to help them stay in place. One method I like for ensuring the base cabinet shims will stay in place is to caulk around the perimeter of the cabinet base, before the moulding is installed. This also keeps water from seeping under the base cabinet if you spill, or when mopping. (I caulk again after the base moulding is complete)

Here is the 800 number listed on the installation flyer. Style SelectionsTM - 1-877-888-8225 and maybe this article will help http://www.consumerreports.org/flooring/breathe-easier-about-your-flooring/

If, they nail it, yes, the plastic will be compromised. No point in adding it, then. Method 1: (2 1/4" total build up) If, plastic will be used for vapor barrier. Grind and levl slab, lay plastic onto floor and up the wall 6-8", float two layers of 3/4" advantech over the plastic: glued and screwed 1 1/4". Then glue and nail assist the 6" live sawn oak. Alllow 3/4" of expansion gaps all around: 1/2" under dry wall and 1/4" under base boards. Trim plastic. Method 2: (3/4" total build up) If, you don't want the extra height. Grind and level the slab, Gaps, cracks and corners should be caulked, apply 2-3 coats of epoxy primer (Sikabond or Pallman) onto flooring and up 3" of base of walls. Then using a glue rated for 6" or wider solid flooring and glue the "live sawn" down. Allowing 3/4" expansion gaps Your only issues will be moisture from above. Climate control will still be needed.