New floor in mud/laundry addition

[HilltopRehab]

Condensed version:
The existing slab is fairly flat and probably more level than it should be, and while it does get damp in storms, I don't have water coming onto it. It's very solid and has crack control joints, with zero appearance of any cracking at this time. I suspect it to be at least 30 years old, and without rebar reinforcement. TBD as to whether there is any perimeter footing at all, I bet not.

2 questions:

1. Is it outlandish to think that the cost to have a footing put in where a new wall will be framed is worth saving, instead putting the wall right where the posts currently sit with perhaps a course or two of block?

2. With constraints on exterior grade and the elevation of the first floor of the house, sleepers will/would need to be placed on top of the slab, followed by a subfloor, onto which I would prefer to have a tile floor. What particular concerns should I be bringing up to a contractor regarding that structure, and could I watch for during the build? Shimming of sleepers comes to mind, as does method of insulation.

These may or may not be outside of the requirements for permitting. I'm somewhat under the impression that contractor(s) could "talk the inspectors into" agreeing with their logic in a number of approaches, including "replacing the existing 4x4 post 'wall' with a conventional stud wall" on the edge of the existing slab.


Context:
I'm at the planning stage for a small addition which will enclose a room underneath existing roof, where a decades-old 4" concrete slab currently sits on grade.
The space is adjacent to the garage and kitchen on two sides, and the driveway and back yard on the other two sides. Garage wall is 2x framed on top of a concrete stem wall, and kitchen wall is the current home exterior - CMU wall with painted stucco.
The roof is possibly an addition from when the "patio" was extended from landings at the kitchen and garage entry doors into the full ~10'x18' space between each wall. It extends from the garage roof, a couple feet above the garage wall top plate, out to what I'll call the rear of the patio, the 18' dimension, where it is supported by a questionable setup of 4x4 posts and beam, with the posts sitting right on the edge of the concrete slab. I don't believe it's anchored/ledgered to the house where it runs along the kitchen wall.

Such a project is perhaps within my abilities, technically, but the amount of work/time is far beyond what I'm willing to sign up for at this point in life.

I've reached out to contractors and gotten bids, and I'm fairly sure who I want to go with. I'm coming back to this community to put my thoughts out there and get a little feedback on the build.