the big gray one is "A" (it has the lever on it)
yes, you can use those wires, and the metra adapter actually recommend it
there are a few ways to strip it. Personally, I like "dragon head" stripper (or you may find them as automatic stripper) as it wont damage the wire. But chances are you don't have them. So what i would do is get a lighter, and heat up the stripping for a few seconds (don't burn it) then take a pair of wire strippers and gently pull it while squeezed. If done properly, the copper underneath will still be intact and the insulation is removed. Then get a pick tool, and pierce the copper wire. Run the wire from the mestro in the loop you created and tie it tight around the factory wire (loop and swoop method, or military splice). With this method, you really don't need to solder.
also, it looks like the factory wires you need to splice are white and pink, but verify with the pin possions