2002 Sentra SE-R Spec V, 160k miles, only mods are a JWT Popcharger, Apexi N1 catback, Centerforce clutch & Kenwood head unit.

These problems have been going on for a couple months and I have tried to figure it out but I am coming up with nothing. Since I bought it about 2 years ago I would get occasional hard starts. Crank, turn off the key, then crank again and it would start. About a week ago it started an erratic idle and after warming up would stall at idle. I replaced the fuel pump with a new Bosch unit and it runs fine again and took care of the hard starts. I never got any CEL until I replaced the fuel pump, now it is throwing a code for Fuel Temp Sensor Circuit High Output.

At times I also get either static or a whine that gets louder as the RPMs increase in the passenger front speaker. I have checked the wiring to the head unit and all of the connections are good (I soldered them when installed).

Also, occasionally my headlights, taillights, and interior lights dim & brighten, usually only when the electric fan kicks on.

I have replaced the negative battery cable and cleaned the spot where it bolts to the inner fender. The positive battery post has turned black, I thought maybe it was arcing so I had someone start it at night while I watched but didn't see anything. The battery and alternator both test fine. Months ago I found a ground wire from the transmission to frame was barely hanging on, so I made a new ground wire and replaced it.

My questions are:
1. What could be causing the CEL with a brand new pump? I am assuming the temp sensor is part of the new pump assembly, so could that just be faulty from the factory?
2. What could be causing the static/whining in my speaker & the lighting dimming/brightening?
3. Anyone know why my positive battery post would be black? I've never seen this before, so I am not sure what would be causing it.
4. Could these problems possibly be attributed to the same source, or am I overthinking it?

Thanks in advance for any help, its really just a nuisance right now but I don't know if it could be something that could cause bigger problems in the future (fried ECU, electrical fire, etc).

Do you have covers for your positive battery post?
There's a small possibility that it's arcing off the hood or something.
The error codes could be a result of the whacky electricals, I'd try to fix the weird static and dimming first before hunting down the other issues.

No there isn't a cover, the old terminal was all jacked up so I replaced it with a new one a while back. Thanks though, ill get one back on there.

Go through and check you grounds man...I had that whine on my GXE, my negative battery post was coming loose, no idea why it caused that but after I tightened it, the noise went away :\

The sensor is part of the fuel pump assembly, if I remember right there's a separate plug for it somewhere in there, or that might be the Titans :| I can't remember