Ongoing Intercooler Issues

Call for help. My Stang is having issues. The Intercooler gauge will show 180 degrees as soon as I hit the SC. Usually it will stay nearly at that level until I turn the car off. I have had issues with the battery light showing on the dash, and have replaced the battery. I am hoping that my ASSumption that since the SC belt also connects to the Alternator, that these issues may be connected. It also studders pretty badly at a stop, and won't idle very well, sometimes even dying.

I took at look at the Intercooler pump, and it seems shaky, and is pretty loud sometimes. It isn't tightened down very effectively the way it was mounted either.

So, my questions are.

1. Do the issues above make sense that they could be connected?
2. Next step? Do I take to a Saleen authorized dealer and not get robbed?
3. Does anyone know where I might get a pump cheaper than a Ford dealer or Saleen, maybe even used?

TIA