You are going to need to pull permits unless you live somewhere that doesn't have any requirements for them. Since that is probably visible from the road, there is almost no way that code enforcement or one of your neighbors isn't going to see it and report you.
The stairs look like the precast concrete kind and probably are hollow and not attached to your foundation.
The method you are proposing sounds more like building a deck than building correctly for a house. Most likely, to be legal, you'll need to remove the slab and dig down beneath the frost line and build up with poured concrete or with cinder blocks.
If the slab happens go down around the edges far enough to support the weight, fine, but most likely it doesn't. Assuming you don't care about being legal, you could build up a cinder block wall to the height level with the bricks on the existing part of the house, setting them back so that you could brick the new parts at a later date. The bricks from the first place might be enough to recycle. Then build your new walls on top of the cinder block walls.
The nice thing about doing everything legal is that it will let you remove that fire place and any of the columns. That fireplace almost definitely wouldn't be legal for inside use.
You are essentially building a self-supporting flat-roofed shed inside the garage, not adding interior walls to the garage.
You should be able to screw a 2x4 sill plate onto the garage floor. The sill plate is mostly there in case the concrete is uneven. It could be pressure-treated in order to resist rotting from moisture on the floor or in the concrete. (In that case, use galvanized nails to nail the sole plate to it.) If you don't build a floor, I think the sole plate of the walls could be screwed directly into the floor, avoiding the sill.
Since you're in a cold climate, you may want to build and insulate a floor. If so, place the rim joists, then hang the remaining joists with joist hangers, insulate, then glue and nail on plywood sheathing. If the joists go in the short direction and are spaced 16" o.c. you should in theory be OK with 2x4 joists, but the code may require 2x6 as a minimum, and that would leave more space for insulation.
Next, frame the walls individually, sheathe them with plywood or OSB, and raise them. If you have a sill or subfloor, face-nail the sole plate to the floor with 16d nails 16" o.c. Sheathing the walls adds lateral support, and thereby helps keep them square. This is a lot easier to do while the walls are still flat on the floor, before you raise them. Make sure to double the top plate.
Finally, frame an "attic subfloor" as a ceiling for your office. In response to your question, the ceiling is somewhat similar to a wall, but the joists must be hung properly (not just end-nailed like the studs in a wall), and the sheathing (plywood or OSB) needs to be glued as well as nailed. Sheathing this subfloor is essential for stability. As mentioned, if spaced 16" o.c., 2x4 is sufficient to span 6 ft, but your code may require 2x6 anyway.
Check out the framing books at the home improvement or bookstore, or google for "framed floor" and "platform framing". Check your building code for insulation requirements. You will probably need a building permit.
The ceiling height may be an issue, once you subtract 6 inches for a floor and 6 inches for a ceiling.
Best Answer
I assume you are wondering what size header to use for the framing and how to support that header. You should: consult your local building department they can tell you. The old rule of thumb is 1" height of header for every foot of width. With an 8 foot span you should use double studs (jack studs) on each side to support it. So - for a 8' span with 2x4 framing a 4x8 header is minimum but my experience is a 4x10 with a nominal dimension of 3.5 x 9.24 is the smallest size header I would use. These days, contractors use 4x12s for most headers up to 12 in width.