Ane, here's what we covered

Filtered Shade, Good Soil, and a Lime Tree Nearby

This area is where the garden beds will go. Olle Gardens is where I'd source the beds themselves, and Arizona Worm Farm is where I'd get the raised bed soil mix to fill them. These beds will also want some filtered shade, Mesquite or Mulga Acacia would both work well nearby to give that dappled light without fully shading the beds out. This same area is also a good spot for a lime tree.

Privacy Trees, Plus Filling Out the Wall

You mentioned wanting privacy back in this corner, and a few large trees here have died off over time. Mesquite is my main recommendation, it matches the desert feel of the rest of the property. Red Push Pistache and Chinese Elm are both worth considering as well if you want one or two more large trees mixed in alongside it rather than a row of all one variety.

For the block walls here, you've already got Orange Jubilee growing, but it's been kept topped so it never gets much height. I'd add more Orange Jubilee to fill in the gaps, and let all of it grow up rather than trimming it back, that's what actually gets you the coverage and height you're after here.

Big Water Wells, Mulch, and a Hedge Along the Wall

This is a good spot for a fig tree and a pomegranate tree. Same approach as the citrus, pull the rock back and build large water wells for each, then put mulch inside those wells so the roots aren't getting blasted by the sun and the heat radiating off the surrounding rock. Along this wall, I'd also plant Hopseed, it'll cover the wall and help cool this whole area down.

Rock Out, Mulch In, Then Plumeria

This backyard spot is a good one for plumeria. I'd remove the rock and add mulch first, then bring in Yellow Dot as a groundcover underneath to help cool the area down. Plumeria itself will do just fine here once that's in place, and banana would work well in this spot too if you want to add that into the mix.

Fill It With a Tree, Transplant the Agave In

There used to be a large saguaro here, and now it's just empty space. A desert adapted tree would fill this in well, Mesquite, Desert Willow, or Desert Ironwood would all work great. I'd also transplant your existing agave into this area, planted underneath the new tree.

For the transplant itself, dig a wide enough root ball around the agave to avoid cutting into too many of its roots, and try to move it on a cooler day if you can, that reduces transplant shock. Once it's in the new hole, plant it at the same depth it was growing before, agave doesn't like being buried any deeper than it already was, and hold off on watering for about a week to let any cut roots callus over before you soak it in.

For more color and interest at ground level under the tree, Chuparosa is a great addition, along with other colorful native options like Globe Mallow and Baja Fairy Duster. Lantana or a similar colorful groundcover would round this out nicely too.

A Plumeria on Each Side, Yellow Dot Underneath

This spot fits a plumeria on either side of the existing lantana, both will do just fine here. I'd pull all the rock back and put down groundcover in its place, specifically Yellow Dot, which you've actually already got started in a pot nearby, moving it into the ground here will help cool this whole area down.