Good questions there.
As a long time resident of southern Calif in the past, I've got some experience with these problems.
First, to answer your questions in order:
Q1 - I'd leave it alone.
Q2 - If there were cracks in the slab that I could put my finger into, I'd fill the cracks and cover with cheap carpet. If, and only if, the cracks were getting bigger - that is quickly (over the period of only a couple months or less), only then would I think of trying to stabilize the area where it was sinking. I'd immediately look into WHY the land in that spot was sinking (water flow? saturation of the land and slippage along an underlying slope? or if the original lot had a lot of fill put in that area that was not compacted correctly when the house was built (this happens a lot).
Q-3 - That's what I'd do unless the crack was quickly getting larger.
Q-4 I'd NEVER spend that kind of money under those circumstances unless an engineer said the place was in imminent danger of collapse.
Now, in general, from my experience of over 22 years in the Santa Barbara area, where there are a LOT of hillsides. When the cities fill up with settlers, the first settlers there take the best places. Then, over the years (often more than 100 to 200 years) the less desirable areas get filled with houses - the riverbeds, swamps, and the steeper hillsides. When this happens, ESPECIALLY more than about 50 years ago (1970's), the developers or homeowners often just brought in any thing they could get cheap/free, threw it in the low spots and then covered it with a few feet of dirt and built on it. Often, they did not use the right fill or compact it in lifts to make a good job, especially if they were just going to sell the place. These natural low spots or are low for a reason - water drainage. The new fill, over time then either settles or it may start to slide, depending on the underlying strata if it is a hillside (much of coastal Calif is underlied by tilted shale (think earthquakes and tilted slopes caused by these) with several feet of dirt over the shale due to years of dust and leaves, etc. When the rains saturate the overlying dirt and reach the shale the water starts to run along the surface of the shale and the dirt goes with it (causing a landslide). Of course, the best remedy is not to build on slopes like that, but you know some people will do it anyway just like they will build in a riverbed or a swamp.
If you're lucky, your problem is more of the swamp or riverbed type and the settling over the years goes slowly and after maybe 30 years the settling pretty much stops because it's done all it is going to do. However, if the house is on a shale slope, then a wet year , especially after fire takes away the vegetation, could result in a collapse at any time (just look at the collapse in La Conchita a few years ago).
In conclusion, if I had a place NOT on a slope with slate underlying it, I'd fill the crack and not worry much unless the crack got larger. If I had a place on a slope with shale under it, I'd sell it asap, before the next wet season and especially now that prices are up and the govt there has gone nuts-er .
--24.180.xx.xx