Your countertop is very earthy and no white anywhere in it. According to Maria Killam if your fixed elements don't have white or cream in them a cream may even end up looking too white. You then should consider a light beige or light gray neutral. Green beige - BM Manchester Tan, SW Wool Skein. It will look cream because the contrast between your earthy elements and the light green-beige is so high. If these green-beige neutrals don't work with your fixed elements, pick whatever neutral is the most obvious. In her ebook a kitchen she did years ago with this same granite she said the color she chose was too yellow (BM Mannequin Cream) and if she were going to redo it she would have went with a grayed white like BM AF-65 Fossil or green-beige like SW 7028 Incredible White or SW 6148 Wool Skein. ETA - I just noticed your flooring in the kitchen is light. I would paint the cabinets whatever light color relates to your hard finishes. I would honesty just pay for one of Maria's online consults and have her pick the color. I'm not affiliated in any way. I plan to use her when it comes time to painting my cabinets to save me from agonizing over buying samples and comparing undertones, etc. Then putting all the work into it and realizing I got it wrong, at least to my eye, visually. I would try and remove the scroll piece above the stove and if you could change any of the cabinet trim that would be a big visual improvement. And I'll admit I'd honestly paint right over the backsplash. I'm sure some will cringe but it can be done easy peasy. I'd paint it the same color as the new cabinet color. Clean well, gripping primer like Zinsser 123 (water based) or Zinsser BIN (oil based) and two coats of paint. I'd put money into replacing the trim on the cabinets over a splash. I would remove the valances but not sure what I would use there. Maybe woven or fabric roman shades.

James, you are right; this is a highly unusual window install in a mansard, what I call a "reverse dormer". I'd seriously consider building a proper dormer that juts out, even if you leave the window where it is, but you could also move the window out, and create a deep sill inside. This involves peeling back some of the shingles and reflashing, so get a pro if this is more than you can handle DIY!

I would start by posting an Actual picture of the front of the house for starters.

IME, flat roofs are prone to leaks and getting ripped off in high winds. If you decide to keep repairing your flat roof, look for the best roofers you can get. It may be possible to rebuild as a Dutch Colonial style without removing the existing trusses. Consult an architect and a contractor if you are interested in that route. https://www.houzz.com/magazine/roots-of-style-dutch-colonial-homes-settle-on-the-gambrel-roof-stsetivw-vs~16982070