I'm not aware of this being a specific code violation. I have seen elevated garages fairly commonly on hillside lots. We also do them with some regularity where we have a full basement beneath the house. I do agree that you need to think about lateral loading, etc. Although typically, we have return basement walls that would alleviate the concern.
For the design of the framing we typically follow a technical bulletin put out by TrusJoist (TB-105). One very important aspect is not to use TJI joists (which you are not using) as they won't be capable of resisting the concentrated load.
I would check the wood stud wall for the concentrated jacking load to verify that the studs are adequate. We typically frame this wall out of 2x6 and install blocking to brace the studs (in addition to any sheetrock, etc.) I'm not aware of any problems we have had with these garages. It's potential that the wood framing will creek as a car drives over it as the wood shrinks. I think using engineered lumber would help this somewhat.
Waterproofing is hugely critical in these installations. We typically install a water proof membrane between the concrete and the subfloor and use PT floor plywood.
IBC Section 2304.12 states that wood members need to be checked for creep loading where the non-structural concrete floor surface exceeds 4". I typically check it here anyways, but it doesn't usually govern as the members are generally quite stiff in order to meet the jacking load design.
Given the choice I would prefer metal deck and concrete, but have seen quite a few of these out of wood.