I do not know if it is important to understand how halon works or not, rather more interested in Jack's steering arrangement.
However, I say again, Halon does not remove/displace the oxygen from a fire situation if you mean the oxygen is consumed or concentration lowered. The oxygen is still present and availible for reacting.
Halon 1301 has 1 carbon, 3 fluorines, 0 chlorines, and 1 bromine, hence 1301. 1211 has 1 carbon, 2 fluorines, 1 chlorine, and 1 bromine. These are all then on a methane.
Fluorine, Chlorine, Bromine, Iodine, and Astatine are all Halogens, and much more reactive than oxygen. Also call them oxidizers. Ever seen Chlorine react with something?
Fire is a rapid chemical oxidation with heat and light usually as byproducts, the hyrdogen (and other) electropositive (ie H+) free radicals generated usually combine with oxygen causing more heat,light and free radicals. (Fire gases are still widely studied to this day and all constitutents are not yet known/understood)
When Halon is introduced, the heat present immediately breaks down the halon chain releasing electronegative radicals (CL-, F-, Br-). Being more reactive than oxygen these electronegative radicals join with the electropositive radicals and break or starve the chemical reaction (fire). This would happen even in an oxygen enriched atomsphere. Formation of HF, HCl, and other products is a not so nice side effect.
Would it work in a self oxidizing fuel (nitro), yes for the same reasons the halogens are much more reactive than the liberated oxygen., hence the incorporation thereof.
For 1211 there is no known exposure limit for humans, "but concentrations > 4% cause toxic side effects" I would opine formation of HCl, HF, HBr in the lungs and mucous membranes. Not due to the lack of Oxygen.
For 1301, OSHA lists a permissible exposure level of 1000 ppm, and an IDLH value of 40,000 ppm (again the 4%). see
http://www.cdc.gov/niosh/idlh/75638.html if there is a lot of interest.
Air is grossly 21% Oxygen, 79% nitrogen, adding 5% 1211 or 1301 could possibly theoretically lower the oxygen concentration to 20% still plenty sufficent to support life provided there is no acute toxicant, and halon un-decomposed is not an acute toxin.
As for the ban, it is all about the ozone, ozone =O3+, add a halogen and the ozone is gone. Ozone gone is bad.
Again just piping in.