The panorama is technically useful if one knows the property. As the sole source of graphic information it is usually too distorted to convey accurate understanding. It's probably okay for what we're talking about today, but if more photos are needed later, I'd add normal focal length, slightly overlapping photos. We cannot tell where the "clear view from the road" coming into your backyard is. But you did a good job of marking the lot line. :-) For plants to do much in the way of screening they need to get some size to them. A more effective, and generally better looking arrangement is three same plants laid out in triangular fashion. A landscape where everything is a "one-of-a-kind" looks weak by comparison. (Amateurish vs. professional looking.) Try to visualize the triangular arrangement with different plant types on the site. I think the Spruce would do a better job screening the neighbor to the north while the Serviceberry would do a fine job of filter-screening the neighbors to east or west. If you plant in these configurations, consider moving the Cherry into the zone I've circled with a dashed line. I would not plant anything near enough to the Spruce to cast shade on it that lasts for any length of time. Too much shade will destroy the plants surface finish. "...Thuja its only supposed to get 2-3 ft wide." That, my friend, sounds like "famous last words." But you might be able to keep it that way with religiously rigorous shearing. You're welcome.

Ways to screen and add variety without getting too busy. Colors and shrubs styles are arbitrary.

Your back alley entry - backyard combo is a unique hybrid of standard house layout. The landscaping will have to adjust accordingly. This makes the space designed and intended for your private outdoor use semi-public. I am gathering the privacy you most need is for the back screen porch and the back patio slab. First off, no you may not plant a tall hedge along the alley to make the backyard private, mainly because you can't block the view of traffic in the alley. If it is one way I might consider it. Now I want to see if I can work your HOA fence to your advantage. If you like this idea it might be worth haggling with the HOA about it if need be. Start the fence on the house corner on the left behind the screened porch. Put a gate in it and run it across the side yard. Head halfway to the alley, turn left and run the fence to the edge of the driveway. Your screen porch and back patio are now enclosed in their own room. Leave enough space, four to six feet, on both sides of the fence for planting. Ditch the tiny beds between the screen porch, patio slab and drive. They are useless. Leave the driveway side of your new backyard enclosure fully open to the drive. Privacy for this side will be planted across the driveway along the property line. If the HOA refuses this fence layout, the same general line of planting beds will do the same. Grasses are a good choice for your location for some very quick privacy. I would not however do them as a hedge of sorts. That would be dull. The two small trees I see planted, one in each side yard, will need to be relocated to better suit this layout most likely. What looks like a birch tree can be an anchor and specimen plant for the outside of your planted fence and privacy enclosure.

Landscaping a backyard for privacy means placing tall, screening shrubs near the offending property lines ... not close up to the house and patio. (There, you'd want to use low plants or overhead trees, or some combination thereof, between you and the view.) For the screening shrubs, you'd need to account for the varying light conditions, which means using a type of plant that can accept sun or shade, or using a variety of plants, each which accepts the conditions in which they are placed. Since you have a length of property to screen, it makes sense that you would place all the shrubs in a bed and keep them separate from the lawn. If you wished to incorporate any small tree forms in the mix, you might want to place groundcover below them instead of only mulch. (It's an opportunity for adding another element of interest. It could include groundcovers that bloom.) Since you want to screen the CL fence, too, it will be an L-shaped bed. If screening both CL fences, it would be U-shaped, following the fence and lot lines. The bed depth, front to back, should be sufficient to accommodate the shrub dimensions, which is going to be quite large ... so probably 8' or 10' depth. Understand that whatever ideas you are given and wish to contemplate, and possibly incorporate, need to be put in the form of a plan before you do any actual work. So prepare a base plan on which you can work out the ideas. You could begin that by tracing over a plot plan of your yard. If you don't have that, measure and draw out on graph paper.