Rick L,
I'm a bit pressed for time, and there are others around who I'm sure can fill in more details, but, to start things off, here goes answers to a few of your questions. (BTW there could be a certain level of disagreement in the replies to a seemingly straightforward group of questions.)
First, "Nitrox" is the name given to any breathing gas consisting of nitrogen (N2) and oxygen (O2). These mixes are also called EANx, where the "x" is a number. That number indicated the percent of oxygen in the mix. BTW, regular air is, in some situations, called EAN21, because air has 21% oxygen.
The "theory of how nitrox works" in part, is that as you increase
the % of O2, you are decreasing the % of nitrogen. As such, you decrease the partial pressure of N2 at depth, which decreases the rate of N2 absorbtion, and therefore, could have a longer NDL (compared to air) for the same depth. Some people use Nitrox for that reason- longer dives, while others use it but stick to "air" NDLs, as an added safety factor against DCS
However, there are a variety of other concerns to be dealt with - including a fun thing called oxygen toxicity.
Second : your Maximum Operating Depth (MOD), would depend upon the O2 % in your mix. (Again that O2 toxicity thing.)
Third: Cost depends on a variety of factors: the mix, where you are getting it (at a resort in a rental tank vs. from an LDS, or elsewhere).
Forth: Regarding "extra" gear: none really-presuming you have a nitrox capable computer or tables-although there have been a number of lengthy, and hotly debated threads on the topic of "O2 cleaning" for nitrox use. (Regs and tanks may need to be specially cleaned or serviced, depending on the mix involved.)
Finally,"Do you get Nitrogen narcosis? Yes, but the reduced % of N2 does have an impact on the onset.
I hope these short answers have been helpful in giving you some insight regarding some of the facts about nitrox.
You have asked some very interesting questions,which I am sure will prompt more replies than this one.
My biggest suggestion would be to take a nitrox course-get the certification, and there, hopefully, you 'll get in depth answers to all your questions, and to the questions resulting from these answers.
Good Luck,
Miked
PS: As a testimony to my snail like speed at the keyboard, Netdoc got in first- But I'm pleased we agree!!