Tree-age

Green Genie

The back garden is currently looking something like the outside landscape in Logan's Run, but with more brown spots.

I have a few questions:
- What is this 'tree' or 'plant' if it's not a tree?
- How far back should I prune it, when? (I'm in coastal Southern California)
- If I prune it back, will it ever develop much more girth?

Cultural Leanings

I also have a leaning blurtree. How would you prune this beautiful sucker so as to encourage it to develop its left hemisphere?

Ground Control

Finally, the groundcover throughout the backyard is part grass, part low-height, pretty stuff that reminds me of clover but is more akin to what I see in nurseries for sale - not inexpensively - in little pots. If the area will be low-use, what's the downside of encouraging this instead of the grass?