Spider box charging / lights question....
 

So I'm trying to make some sense of the wiring that had been hacked into a little bit from a previous owner.... after pulling up a wiring diagram online, I have to ask: is the battery really being charged ? I mean, I can trace the wire from the R/R back to the fuse, then to the starter relay, which connects to the battery. Is that correct?

Now my other question: the stock red wire for the lights, that is not a 12v DC wire, right? I'm planning on running led lighting, but I'm pretty sure hooking up led lights to AC current won't work.

Any help / clarification is appreciated.