First, the branches in that 'nice' circle - are they in fact at different, or the same level? They really should be all at different levels (and directions, but that's a little less vital). Second, cutting the branches will cause them not to fatten, but then again, why would you want them fat? It's the trunk that needs fattening, tapering well from the bottom, and the way to get that is to leave 1-2 of the lowest branches to grow unpruned for as long as it takes to get the girth you want, and then if that branch doesn't fit with the eventual design you have for the planned tree, it can be cut flush with the trunk. When you say roots are contained in the pot, what do you mean (that none have grown down thru the drain holes yet?)? Containing the tree to a small pot when it's not yet the size or thickness you want is counterproductive, so maybe forget 'bonsai' for now in terms of the pot, apart from keeping it relatively shallow, and use a slightly taller but definitely wider one while it's growing out. I do hope you do have 1-2 good sized drain holes in the pots?

The cat's claw vine, Macfadyena unguis-cati, should grow well in your conditions, and clings by itself. The flowers are vivid yellow. I find this vine to be too aggressive, but if you have it contained, it should be ok. What about training a large shrub into a tree rather than planting a tree? Geraldton waxflower, or Chamelaucium uncinatum, can have a beautiful twisty trunk and branches as it ages. Fatsia japonica might work, but might not have the look you desire, with its large leaves -- but hey, not much mess to clean up. Pittosporum tobira, the non-dwarf type, can be shaped to a smallish tree as well, and you could use the variegated 'Wheelers Dwarf' as underplantings. Ficus elastica - again, contained - could be attractive and tidy as well, will re-grow if it gets frosted. Check your Sunset Western Garden Book for planting around pools for zone 18 or 19 and see what excites you.

Growing a tree near or on your poolside should really be lovely. However, this might cause you more efforts in cleaning the pool every time especially that trees regularly shed leaves off. Good if we only have leaves that are solid as dirt in the pool. But we all know that there are some substances from trees that may color or dissolve in the water causing you to change the water which surely would not be convenient. Why not just use sun shelter or sun sail awnings to add shade.

Again, I can only offer generalities. But tree roots generally grow outward more so than downward. There are rare cases in extremely porous soil, of people finding tree roots at crazy depths, so it's not impossible. But the usual pattern is outward, away from the trunk, the basic idea being that tree roots, like all of life, respire, using oxygen in that process. Not much O2 down in the depths of soil. I can't say whether you will or will not have problems with roots impacting your foundation. Let's see, you're in Cali, so I'm going to guess no basement, the house sitting on a poured slab. As a great lover of greenery in general, I want to tell you not to worry, so I will tell you that....don't worry! Of course, I could be wrong. But yes, I'd prune away branches which are actually in contact with any part of the building, again using proper technique and only target cuts. At least, I'd start with that and reassess later. I'd not think there's any aspect of this which crosses the line into emergency status. And please, I'm not there looking at it, so if some qualified person on site makes a recommendation, listen to them. Don't say this guy on the internet said such and such...lol! +oM