Is there an HOA and if so, what kind of rules regulate things like fences and plantings? It seems like with your wishes, getting rid of the lawn and having a combination of shrubs with groundcovers in garden beds for privacy and ambiance along with paved areas with the seating, dining, and hot tub areas differentiated into sections by planting beds might be your best bet. For inspiration look at a bunch of the projects from the designer linked below, Johm Algozzini of K&D Landscape Management. His patio areas are broken up with planting beds into areas related to their function. I find his work really appealing and far more attractive than the more typical expanse of unbroken paving that is often seen. https://www.houzz.com/user/kdlandscapemanagement Start folders of landscape ideas you find appealing, here on Houzz or in garden magazines or books from the library or from other online sites. As Yardvaark said, more info is needed to make useful comments. In addition to the photos he suggested: What are exposures for sun and shade; what direction does the back of the house face? Generally where are you located, such as state or province and nearest large city? And what USDA growing zone? Do you have access to a plot plan or can you do a screen capture of the house and plot from the town tax website or even from Google maps? The current photos make it difficult to judge access, how much useable side yard you have, etc. Are there views you want to enhance or block such as neighbors behind you or a greenspace? We can’t see what is on the other side of the fence.

Take a couple more pictures. Move to the city sidewalk in line with the front door and take one picture. From the exact same spot pivot rightward and take a picture that overlaps slightly with the first, showing the right portion of the house.

What are the two shrubs that remain? I ask because they seem to be thriving and some plants do not like clay soil. What are the two little trees off the left corner? As Yardvaark mentioned you need to lower the soil level near the walk because five inches of mulch is what is used to prevent weeds. Do not use fabric or plastic beneath the mulch. Over time microbes in the soil will break down the mulch. It is good for the soil. As it beaks down you will need to add more mulch. That is why it is best to add enough plants to cover most of the planted area. Are there any plant nurseries nearby? It is easiest to get ground cover plants in plugs.

It's not likely that a single tree is going to do a good job of providing privacy. This is probably going to be achieved through a combination of small trees along the property perimeter and some large shrubs. (The small trees might also be made of large shrubs since you don't necessarily want to overwhelm yourself and neighbors with a small yard full of massive trees. If you want shade, It will most likely come from large trees that have been limbed up to maintain ground clearance. What do you mean by "privacy wall"? It sounds like you're after a full back yard development. It would be to your advantage to create a plan and submit it here. A simple base plan looks like this, except that it will show your backyard.: Include the existing trees in the base plan, showing only dots for their trunk locations.