Yours is a pretty popular sink design currently for a two-bowl type. Generally this type sink is referred to here as a 1-3/4 sink. I love mine and it has the same dimensions (same depth of sinks) as yours. As far as space between the faucet and backsplash...just make sure the faucet design you picked out has enough room to operate the on/off handle without it hitting the backsplash and without you scraping your knuckles as you work it. HD or fabricator/intallers should able to tell you if it will work.

Sconces mounted on mirrors can look good, but I'm not sure that mounting a sconce on a wide wooden surface in the middle of the mirror is a good choice -- esthetically or practically -- particularly with that nice, formal cabinetry. Why don't you simply dispense with the wood and mount the sconce directly on the mirror? I have a pair of sconces mounted on a 5-1/2' wide mirror in my powder room. I also get better light distribution because the light at the rear of the sconce reflects off the mirror.

Manual says minimum of 2 5/8" for door to open 90". For the full 125" opening, clearance would need to be 10". We tested it yesterday by moving the fridge around and found that about 4" would be enough to open the door a bit past 90" and all drawers and shelves can slide out fully should I ever need to take them out for cleaning. One possible option is to put in a narrow utility cabinet in the corner and have the fridge go next to that. Ikea's narrowest is 15". I'd need to double check exactly where the water line is to make sure it would still be in the fridge area and not get stuck behind the utility cabinet. That may be my best option to avoid a large filler. Thanks all!

From a door function standpoint, leave 4" minimum from the corner. This gives you enough space so that the door can open 90 degrees without having the door lever hit the wall. 6" is also common too. You don't want to leave too much space or you are just wasting usable wall and floor space in your room. However, from a maintenance and aesthetic standpoint do head bpath's advice above. The trim should either leave at least 3/4" to 1" wall reveal from the corner or be right up against the adjacent wall. leaving a small space is going to result in an awkward strip of wall color and will be difficult to maintain going forward. In our current house we have a few of these conditions where it is tight between the casing and corner. The last owner wallpapered and we have had extreme difficulty getting old wallpaper out of these corners. In some cases the trim had to be taken off to get good paint and stain coverage on them too.