Hi Karen: Concern over the integrity of your foundation is wise. Failures here tend to be serious or worse if not resolved early.
You address several issues....
Basically, a foundation is composed of a footing, which is usually at least 12 to 18 inches wide and 8 to 12 inches deep (depending on the weight of the house), the top of this is always located below the frost line for that area.....and for San Diego, I believe this is 12" below grade. There should then be a poured or cinder block wall that sets on the foundation and rises up at least 6 inches above the ground, upon which the house wood framing is built. A beam (or beams) run from one concrete wall to the othe side. In a house with a crawl space (like yours), these beams are supported by 4X4 posts, which rest on pillars or concrete pads, and are spaced 8 feet or so apart.
Your foundation should not settle unless the ground beneath it was not adequately compressed; poor drainage could worsen but should not cause this kind of problem. The framing of your house (sill plate) should be tied to the foundation using anchor bolts through the 2X4 or 2X6 that rests on the top of the concrete (or block) wall. If you cannot find any anchors, installing them should be a top priority. Adding more posts/pillars will not help much in holding the house to the foundation. But with the number of earthquakes that have occured in S. Calif since 1920, it is highly unlikely that your house is 'floating' on the foundation, as it would certainly have 'floated' off by now.
congrats on your new house; I'm sure you'll enjoy it.