Welcome,Thanks for the very detailed information. If there is 12 volts to the batt wire on the back of the alternator, and the fuses are good, then Every single thing you mentioned points directly at the alternator not charging. If it was charging, it would read 14.5 volts with the engine running at high idle with or without any accessories on. A 12 volt system requires 14 volts to be charged. It will need replaced. I know you mentioned t has been replaced but i have seen many, many rebuilts fail right out of the box.
Check over the wiring real good. See below.
If you have further questions feel free to reply.LJ
Okay - I'll get another alternatorThanks and Best Regards XXXXX XXXXX