Foundation modification question

My house is on a slanted hill in SF (an earthquake area). I'd estimate the hill to be between 30-40 degrees. The house is a 2-story SFH built in the 1920s. The slope is higher on the left, and lower on the right. As a result, the pavement in the garage is not level. The foundation on the left side is higher than the right side. It is a 2-car tandem garage, the area where we want to build the room is inside to the left of 2nd car.. (so afterwards, one car, and rooms in front of it)
The garage looks kinda raw, with no dry-wall. We want to build some storage room in the garage, but as it is, there isn't enough height clearance. I'd estimate about 6-ft to 7-ft, depending on where you are in the garage.
To make the floor level within each proposed room, some contractors said they need to break the existing concrete floor, dug out the sand (we live in a sandy area), and as a result, the base of the foundation on the left side (higher) will likely be exposed, so they will "expand" the foundation down-ward (put something to support the current foundation while purring another one below). I estimate they will need to dig down about a foot on the left side to make it match the middle of the garage (not the lowest point, just the middle).
Now the contractor said it's not a problem, they've done foundation expansion this way. But I am just a little worried. Does this sound safe? Especially on a slanted hill?
The current garage, although doesn't look its best, feels very solid. The house appears to have survived the 1989 SF quake without much problem. I have 2 worries:
If we dig down, and assume the contractor do a good job, the existing foundation will be sitting on a new foundation. Not the entire left side of the house, but perhaps a 10 foot section. (how tall will the new foundation be, I don't know, probably half a foot?). But during an earthquake, won't the upper foundation move freely since it's not bolted down with the foundation below? This seems risky to me. right now the foundation can't move because the garage floor next to it is concrete and pushes against it.
My 2nd worry is, my next door neighbor to the left (the houses are next to each other), his garage floor is obviously higher than mine. So it seems to me currently there is more pressure (soil) on the other side of the left foundation than on this side (empty). If we dug down, there will be more pressure, during an earth-quake, will the foundation just tip-over to the right?
And to finish it off, the contractor we will be hiring is not licensed. Hiring licensed foundation contractor to do the foundation work is out of our budget. The current contractor is kind of a general contractor that will be doing the dry-wall, etc.. He definitely have experience, just not licensed probably due to language problems.
Should I be worried about the foundation update? Without breaking the existing garage floor, it's hard to make the floor level, and breaking the floor means the higher side's foundation will be exposed and needs to be expanded down.
Apologize for this long email, my parents wants to divide the garage into some rooms to make better use of it, but it's just the options seems limited due to the slope in the garage and the low clearance.
Personally I am opting for just doing whatever we can without touching the foundation or the floor, which seems to be in good shape. But my parents wants to build some rooms so they can potentially rent it out when they retire soon..
And one last question, for foundations, are there different grades of concrete that needs to be used?
Thanks a lot!
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