Yes you could do that. Just make sure that if a plant gets say 6' tall that you leave that much room from the trunk to allow that plant to grow with crowding each other or other plants.

This could work. Perhaps on a smaller scale.

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.

Where do you need privacy and where would people be whose view you want to block?

With surrounding grade levels already happily established. raising the patio level with any material is not without potential problems ... trapping water, creating trip hazards or awkward accessibility. It would be easier to limit changes to the 2-D shape and then treat the surface cosmetically with some type of coating or other surface treatment as there are some options.