Probably ok as long as the rim area is insulated. Space between the XPS and batts will permit air currents that reduce the effectiveness of the batt insulation. I would prefer to box and keep the wall as tight to the foundation as possible. Otherwise, fill the space with low-cost EPS insulation. Here is a link that might be useful: US Dept. of Energy R Value Recommendations

mat r Poly covered batt insulation in the basement walls can fail in as little as a year, saturated with trapped water vapour feeding mould in the drywall. (See brewbeer's link above.) The bottom plate does not deform when it's on top of XPS. Just score and snap sections wide enough to fit under the plate. (I used to use Super 6 vapour barrier; this keeps vapour from wicking up, but doesn't do anything if you get standing water.) XPS between the studs isn't ideal, but it sure beats most anything else. If there is space between the foundation wall and your stud wall, it would be better to slip in even half inch sheets along the wall. In that case, and that case only, you could safely use batts on the warm side of the basement wall with or without a facing. Just slitting the facing on the batts and putting them in by themselves is inviting trouble. (Following "best practices" at the time, I used to put a poly sheet on the concrete wall and leave it loose at the bottom; the idea was that the moisture on the wall would roll down and somehow get into the room and evaporate. A lot of hoping! And by slitting the warm side barrier, you'd be counting on the vapour going through the insulation, condensing on the warm side of that same poly and running back into the room as water. Long term, I bet it will fail too.) Above grade, Building Science Corp. says unfaced batt insulation is acceptable. (See Link above.) Electrical boxes. Just mount them on the 2x4s as on any interior wall. Do not attach the 2x4s to the walls; use plates (2x4 laid flat) top and bottom. If you have a concern about the wall thickness, you can use 2x3. Or even 2x2 light steel; but only where there is XPS on the wall and as little air movement as possible, as the steel will condense any water vapour that gets into the wall. Number of fasteners for the floor plates--every three to four feet. While XPS is my preference, Building Science Corp. says that EPS is also acceptable. But it has a lower R value per inch. Finally, be sure to provide mechanical dehumidification during the summer months to keep the moisture levels down. If I were to treat the walls first, I would use a permanent product, preferably a crystalline waterproofer in a slurry coat.

"Have you thought of changing the wall studs to 2x6" rather than 2x4"?" I don't wish to destroy the wall on the far side. I have a large map wallpapered to the other side. I could build out with a false wall for some additional distance, but I don't see that as necessary since I can do at least 3-1/2"x14" (almost equivalent to a 8" round duct). Plus, I found a standard "Straight Register Boot" to transition to 8" diameter. I believe 3-1/2x14" equates to about .05 friction loss for five feet). I just don't know what 2200-2500 FPM will equate to in sound level at the hood. I foresee cutting a 4x15 opening (or bigger), at the back of the hood. I am re-reading rjpjnk's post and I remind you I only have five straight feet till it feeds straight into the fan venturi. I found this is an engineering handbook: Duct velocity should be between 1500 and 4000 FPM  Hood velocities (not less than 50 FPM over face area between hood and cooking surface)  Wall Type - 80 CFM/ft2  Island Type - 125 CFM/ft2  Extend hood beyond cook surface 0.4 x distance between hood and cooking surface Filters  Select ï¬lter velocity between 100 - 400 FPM  Determine number of ï¬lters required from a manufacturerÂs data (usually 2 CFM exhaust for each sq. in. of ï¬lter area maximum)  Install filters at 45 - 60°to horizontal, never horizontal Using this as a guide I think an average 400 CFM for general-purpose venting @ 1500 FPM means that I am well covered with a variable speed 1000 CFM external fan and 8" duct area. I'm guessing that at 1500 FPM it will be pretty quiet. The old Vent-a-Hood units are supposed to deliver 300 CFM each and I usually only use one. They are super noisy at near my ear level and 18 inches away. The air passes through a 3-1/2" x 4-1/2" rectangular opening! That's small and seems to equate to almost 3000 FPM! I guess it's no wonder they're so noisy... Am I missing anything? Bad calculations or asumptions?

Brickeyee: Your comments are appreciated. I took some pics today. Here is the door. It is on an exterior wall, it used to open to a covered porch: That wood you see is the back of wood siding. (winter hasn't hit yet, so we have a couple months to address this) And here is a pic of the door opened. There is 7" between the edge of the siding and the outside edge of the moulding: Is seems like a shame to take off all that original moulding and we were just thinking some sort of niche might work here. Does anyone think that spray foam to seal up the any air gaps then a piece of rigid insulation followed by finish plywood or luann of some sort may be sufficient, here, as the back of our niche? Or should we forget it and fill it in with insulation, drywallpatch right over it and get ride of the mouldings? Are there any other features we could turn it into?