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.
My guess is that it's either a sandwich beam (wood sandwiching a steel plate) or simply an i-Beam. When you drill, are you drilling through wood or just sheetrock?
If it's an actual i-Beam, you could hang it with some sort of clamping device.
I wouldn't trust dry-wall anchors for hanging a punching bag. Dry wall anchors can hold quite a bit, but not the active load of a swinging punching bag.
Best Answer
2x's laying flat as opposed to on edge are going to bend or break when weight is suspended from it over time. The longer the board the faster it will compress or fail. To remedy this problem you must add support to the existing framing members. I think the simplest way is to install additional 2 x 4's (on edge) attached against the edge of the original 2 x 4's. It should have a "L" shape profile. You didn't mention the span of the rafters, but you may consider adding webbing above the platform. All this is are lengths of 2 x 4 attached to the platform joists at one end and the other to the mating roof rafter above. This is probably over kill, but still another way to prevent a failure.