Hi there. Nice home. Yes there are many lime formulas and techniques to white wash a house on the internet. Does your brick have a smooth finish to it, is it porous? A way to test this is to run water over the brick, does some of the water absorb into the brick? Does the brick stay damp for a bit? If so then your brick will work well with lime washing. If not then lime may not work well on your brick. So test a small area first. I know this may be a bit bold for you but I would consider white washing the entire house. I personally like homes in one color. It gives it more of a classic look. Also it would like very nice with the different textures of material( brick and stone). If you feel that might be a bit too much start with the brick first and see if you like it. Start with thin coats then keep applying. I feel the stone needs to be softened up a bit. So add a few thin coats over that as well. I would personally go all white and add plant, shrubs, trees and vines next to the house to break up the wall height. Plus that would really make your landscaping pop up against that White House and give it character. There is a lime formula that is mixed with white Portland cement that a world renowned architect Ken Tate gave me that we are using on our home. I've done some sample walls and it turned out great! It sort a tad thicker than a straight lime wash and it gives the brick a soft edge. It looks like it's been painted 100 times. Just like the old buildings in Europe were limed washed back in the 1800's. The mix I use is 4 parts white Portland cement and 1 part lime, 4.5 parts of water. Should have a consistency of whole milk but not too thick! You can mix pigment in with any formula but we choose not too. It comes out white but with a very soft gray white. I tested it with the reverse formula and the lime was Greek white. As light hits the lime, light reflects twice as much. So the more lime the brighter it greats unless you add a pigment. Some people like some brick sort of bleeding through, however we are covering all our brick so that it's all white. If you plan to go all white, you'll need several coats to cover. Sounds like you are adding shutters, good idea. That will give the house character. Also make sure when you buy or have them made to make sure they are sized properly to actually cover the window if they were closed. Not too small. I would go with a dark hunter green on your shutter and keep your windows and window trim the taupe color. And other trim white. If you go the lime route make sure you find someone that knows what they're doing. The most import thing when applying lime is to keep the wall wet down but not standing water, after applying the first coat of lime, let it dry 24 hours between coats. If you don't let it cue long enough between coats you'll have crazing (which are a network of very fine cracks). And make sure it's done between outside temperatures 50-90. Morning and afternoons. Try to not apply it when the sun is beating down. You don't want it drying too fast. We are liming the house ourselves, I know it's cray but we can't fine anyone that can do it. Also if you don't want to mix this yourself there is a company called Roma ( google Roma lime wash) they have premixed lime putty formulas and they can also mix in your pigment of choice. Just add water and your ready to start liming. Good luck and let us know how it turns out.

Try pressure washing the stone and concrete. Would not paint or white wash either. You could use the existing steps and sidewalk as a foundation to which you could attach pavers of your choosing. https://www.youtube.com/watch?v=c385eN9Tvqw Gray siding wouldn't necessarily be the best color with a brown roof but if you're hoping to swap out the roof within the next few y ears, you might be able to paint the brown roof shingles a dark gray or black until you can replace it and go ahead and get the gray you prefer. https://www.google.com/search?q=How+to+paint++roof+shingles&tbm=isch&ved=2ahUKEwiyy_zbmrnoAhXGM1MKHUrTDcQQ2-cCegQIABAA&oq=How+to+paint++roof+shingles&gs_lcp=CgNpbWcQAzIECAAQGDoECAAQQzoCCAA6BQgAEIMBOgYIABAIEB46BAgAEB5QujlY3Wtg3nVoAXAAeACAAf4BiAHiDJIBBjEzLjEuMpgBAKABAaoBC2d3cy13aXotaW1n&sclient=img&ei=VS99XvLMEcbnzALKpregDA&bih=628&biw=1366 Your window frames are dark. Would not add shutters. Consider adding white frame boards all around the windows instead. For the large blank area on the left, consider adding pressed metal exterior wall art. https://www.touchofclass.com/marielle-tree-wall-art-brown/p/H373-001/ https://www.google.com/search?q=pressed+metal+exterior+wall+art++sunshine&tbm=isch&ved=2ahUKEwj0sbaznLnoAhVCh1MKHXlRDRoQ2-cCegQIABAA&oq=pressed+metal+exterior+wall+art++sunshine&gs_lcp=CgNpbWcQA1CU_wRYtIsFYMDvBWgBcAB4AIABXIgBzAWSAQE5mAEAoAEBqgELZ3dzLXdpei1pbWc&sclient=img&ei=GTF9XrTBB8KOzgL5orXQAQ&bih=628&biw=1366 When your new siding and painting is done, your landscaping choices will make a huge difference. If Aucuba bushes will grow in your planting zone, they would be a good cover for your stone -- they keep their leaves and look good year round.

You might be thinking of limewash from Romabio: https://romabio.com/masonry/limewash/ageless-beauty/

any stone safe cleaner will be fine. mortar is just a cement based mixture. Have you applied a sealer to any of the bricks? maybe clean them, let it dry, and apply a penetrating sealer that won't change the colors? this is safe for marble and any stone. but always spot test. some of the other masonry cleaners are acidic. but I don't think you need that.