neoz42 (./1) :
which laguage do we use ? asm, C ou another one ?

Either C or assembly is usable. (Check the Development tools page on the wiki) C is a bit easier to get stuff done with, especially with DATlib.

neoz42 (./1) :
is it possible to do some "reverse engineering" to get some datas such as graphics or sound on an existing game ?

Yes it is. A few tools exist to decode/encode graphics and sound data. (I forgot to put links to the decoders on the page, oops.)

neoz42 (./1) :
How to compile / test my code ?

Compiling will depend on what language and tools you use.

For testing, the easiest way to test is to use an emulator (like MAME). You'll want to have a recent version, so you don't have to recompile the entire program when you need to make changes. Instead, you'd edit the neogeo.xml file in the hash folder and add an entry similar to the one in this post. (MAME will tell you if the MD5 and SHA-1 hashes are wrong and will give you the correct ones. This will happen a lot if you're testing program/.Px/.PRG changes.)

If you're targeting the Neo-Geo CD, you can either burn a CD, or (if you have the CD Universe BIOS and the USB PC-2-NEO cable) upload it from the PC.
Cart systems are going to require de-soldering chips from an existing game and replacing them with your own chips.

neoz42 (./1) :
what is the difference between the files we found in a roms archive (Cx, Mx, Px, SPx, Sx and Vx) ?

Cx: Sprite graphics (interleaved, so e.g. C1 and C2 make up one part of the sprite data)
Mx: Music driver (Z80 code)
Px: Program ROM
SPx: not fully sure, but possibly used for patches on official games; you typically don't have to worry about it.
Sx: Fix layer graphics (displays over all other graphics)
Vx: Sounds (ADPCM-A and ADPCM-B, though the latter isn't available on CD)

neoz42 (./1) :
is there any testing program, example code or tutorials to make my first steps ?

There are a few bits and pieces on the wiki; I've released a few assembly-using productions in this forum, and I'm also working on an assembly language "from basics" tutorial (WIP version here).

Happy hacking!