The tree now in the lawn is large enough that you can stand to remove another bottom limb or two, with the idea of developing the strong central leader/trunk and letting more light below in order to keep the grass growing healthy. Having a row of shrubs, a hedge, marching across and in front of the foundation is certainly one way -- a time-honored way -- of treating the front of a house. And surrounding the entrance sidewalk with a planting, as if creating a little pen that is the path to the steps, is another. But I think both of these ways ultimately work against making the front of the house look more inviting and in general, happy. I think a better way is to arrange the bed line so that it "funnels" one's view toward the entrance. Filling the bed with the largest plant material being farthest away from the entrance helps with this view-funneling effect, as does having the lowest material nearest the entrance. Annuals, with lots of color, is a good choice for the latter spot because it contributes to the happy factor. (The little multi-trunk tree would be made out of a large shrub so that its size stays small. As well, it shouldn't be a shrub with a propensity to sucker badly. Lilacs are borderline on this.) Instead of the hedge of shrubs covering the whole front, I like to coordinate them to windows, thinking that it's enough. And it avoids the smothering-in-shrubs look that comes in a few years. It's easier to maintain, too. What I've shown in purple is likely some kind of perennial mass. The colors or textures don't mean anything more than differentiation of one type plant from the next. Dividing the bed from the lawn with a border of brick/pavers (as you show in 3rd picture) is fine as long as it is sunk flush into a mowing strip like that. (I widened the walk/landing a little. No charge on that. :-))

I know that if I lived there I would be sectioning off the lawn from bed and getting rid of grass everywhere there was slope or shade. I see a little of that going on, but not near enough given the terrain and tree cover. In making such "islands" one wouldn't want tree trunks to be at or near the edge. They should be solidly in the island. Since you already have English ivy and the areas look to be quite sizeable, I'd continue with it. It is easy to grow a lot from making cuttings so you wouldn't need to buy it. The picture is advice on where to put trees, shrubs, annuals, perennials and groundcover. The color doesn't mean anything more than being able to differentiate between type plant and another.

You should paint the gutter downspouts to match the brick. With white window trim, it seems unnecessary to paint the white fascia and white horizontal gutter. If the well and septic tank are NOT being used, they'll only be a potential impediment to your digging not a prohibition of it. If you run into an unused well or septic tank pipe, you can simply cut through it. Electrical wires would be a different issue. Rather than a "patio" against the house, you might well be better served to create a front porch all across that "area under question" between the two front wings of the home -- a porch that you can use by exiting via the front door rather than adding a new forward facing door. Even if you stay with the patio idea rather than creating a wide front porch, resist the temptation to add a second forward facing front door to your home. If you create a patio beside your front porch, make it larger than the "area" of loose dirt and don't limit it to a rectangle against the home. A larger window in the dining room might, however, be worthwhile -- perhaps even a different kind of window if you want to create a pass thru to your porch or patio. Remove the loose soil -- what appears to be rich planting soil -- from that "area" (to be repurposed for either filling in a low place or to be used in a raised flower bed elsewhere). You want to have hard ground and stable rock beneath your new porch or patio. For a porch, if you choose a treated deck board floor, you'll need to have the ground beneath it sloped away from the house. If you choose a concrete porch floor -- which which will last longer, be easier to maintain (and, therefore, be more economical long term -- that removed soil will most likely be replaced with gravel before any concrete floor is poured (rather than pouring a thicker slab of concrete). A concrete floor porch will require a footing and foundation across the front and, if it extends beyond the two wings of the house, on the sides as well. Any removed loose topsoil will likely be replaced with gravel before the concrete is (rather than pouring an unnecessarily thicker concrete pad). You'll want any porch or deck or patio to be not less than six feet deep. That depth surface will enable you to set chairs on it and still walk by them the full length of it. For a porch roof, you could raise the front half of your roof between the two front wings of the home to cover the area of the new porch. https://rgbconstructionservices.com/hip-roof-vs-gable-roof-best-home/  Another option would be to create a concrete porch floor between the two front wings of the home that extends to a point even with the front edge of the front wall of the home -- but ONE step down from your existing stoop floor -- to use as a part of an uncovered patio now but that might be covered for use as a porch later. You could then create a third patio level with a sidewalk (that is at or closer to existing sidewalk level) to be used as your permanent patio, with that sidewalk leading lead away from the front entrance toward the left side of the yard (away from the driveway side of the yard). You could face the front edge and sides of both the existing front stoop and the new future front porch with stone (or brick) https://www.google.com/search?q=Front+yard+patio+by+porch&source=lnms&tbm=isch&sa=X&ved=0ahUKEwjkkPaJkovlAhVBSN8KHeQNAQwQ_AUIESgB&biw=1328&bih=617#imgrc=EZ5cIofdfse1pM:&spf=1570485418994 and then use that same material to begin to create your actual FRONT YARD patio. https://www.houselogic.com/photos/yard-patio/front-yard-patio-ideas/slide/patio-as-focal-point/

Looks like a great spot to hang out with your dog! Narrow urban yards can be challenging, but careful planning can maximize a small space. See photos of an urban garden in Chicago here. Remove existing shrubs to create space for a pathway that connects the front and side yard. Establish a focal point at the corner, similar to the photo here. The focal point can be a planter, fountain, garden art or statue that is visible from the front and side yards. Your stone pathway can be laid out from the front porch to the side of the house, ending with a petite patio area with a bench or a couple of chairs. Seating could also be added with a bench that provides handy storage for cushions, dog toys, and a water bowl like these. Finish the front with ground cover between the stones as shown here.