Dude, you're in way over your head, but you can fish without stapling, you cannot run romex on the surface of sheetrock, and the switch can be on the surface, but the wire still needs to be protected, in the wall or in pipe. You can run MC or FMC on the surface.
I'd like to recommend some good reading material, http://www.amazon.com/gp/product/0877659656/ref=as_li_ss_tl?ie=UTF8&tag=undehomepowe-20&linkCode=as2&camp=1789&creative=390957&creativeASIN=0877659656
Edit: When I do work that I am not familiar with, like intrinsically safe or solar voltaic systems, I start by reading the relevant code section. I guessed you didn't have a code book because the NM, section 334 is only 2.5 pages long.
334.10(3) Uses Permitted...Cables shall be "concealed in walls.."
334.30(B)(1) Unsupported Cables..permitted where "fished between access points.."
334.15(B) Exposed Work Cable "shall be protected by RMC, IMC, EMT, SCH 80 PVC.."
2nd Edit: "Fished between access points" is in the paragraph titled "Unsupported Cable", seems pretty straight forward: "cable shall be permitted to be unsupported where the cable: (1) Is fished between access points through concealed spaces in finished buildings or structures and supporting is impracticable." Maybe your problem was just finding it, in the wiring materials sections xxx.10 will be "Uses Permitted", and xxx.30 will be "Securing and Supporting".
And to helpful about the supporting the box, look for an "old work box" http://www.amazon.com/Carlon-BH614R-Ceiling-Diameter-24-Pack/dp/B000LPTDNE/ref=sr_1_3?s=hi&ie=UTF8&qid=1339277237&sr=1-3 , or for the switch http://www.amazon.com/gp/product/B000HEKQMQ/ref=as_li_ss_tl?ie=UTF8&tag=undehomepowe-20&linkCode=as2&camp=1789&creative=390957&creativeASIN=B000HEKQMQ
Couldn't find bx in my code book, do find AC in section 320, check 320.10 for uses permitted, and 320.30 for support.