How would you put up/frame a wall where the 2x4 studs are turned flat to make the wall 2" thick? One especially tricky thing is that (it seems that) all nails must be toenailed since a 3.5" long 16d nail isn't long enough to attach the 3.5" tall plates to the studs. Are there any suggestions on how to avoid toenailing or how to toenail effectively with a nail gun so that they go in at the right angle to grip well, not split the 1.5" thick wood and not stick out the other side?
If you're willing to put a little extra work into it, using screws instead of nails can really help make this kind of "light" framing much more durable. It's a little/lot more time consuming, depending on how much you love your power drill, but well worth the extra time, in my opinion.
Are the top and bottom plates already installed? Could you use a 2x2s for the top and bottom plates? Then you could nail (or screw) through from the outside of the plate into the stud.
An easy way to complete a wall like you describe is to build it flat on the floor. That way you can screw or nail the studs to the plates through the plates. I recommend installing a separate plate on the floor or across the upper joists first. Floor usually works best. Then simply measure the shortest dimension from the floor plate you just installed to the joists and build your wall to that measurement less 1/4 inch. Now you can stand it up usually without the angle getting hung up on existing ceiling and walk it into place. If you don't use the extra separate plate, it is almost impossible to stand it up into place. Attach it to which ever plate (top or bottom) you installed first, then shim it to keep it stable and plumb it as you nail it to the bottom plate or the joists. When you build the wall on the ground, lay out your 16 inch centers etc. Flush up the second plate to the one you just marked and transfer the marks to other plate with a square. Now you know where to place the studs between the plates. This method is the most common practice for building non-load bearing walls in an existing structure and works with any size lumber you want to use.
I've done this before and typically I'll frame the whole thing with 2x2's (top & bottom plates + 2x2 "studs").
It can be tricky finding straight 2x2's though, so often I'll just buy 2x4s and rip them in half on a table saw.
I would consider using tie plates with 8d nails. Perhaps T-shaped or triangular plates. Be sure to check your local building code.
Use 2x2 top and bottom plates and 2x4 studs. Who care if the 2x2s are a lil warped... they're gonna be. Just straighten the wall as you nail it down or tapcon it or whatever then staighten the top to your line and nail to the joists or blocking. Done. No ripping anything.