it also looks like your alternator prematurely failed due to some sort of leak, my best guess is a leaking axel boot, so if you replace the alternator and leave that axel in there you will have another alternator failure not to far in the future. I just had this issue, my car had a brand new motor craft alternator in it when I got it 25k miles ago, the alternator quit because the axel started to leak all over the alternator. Replaced the axel and the alternator and haven't had any issues since.
Just saw your most recent post, dont get any 3rd party reman alternators, you will have problems very soon after. I personally have witnessed people putting in Pep boys or bosch or autozone brand alternators and having to go through 4-5 of them before they finally get one that doesnt throw a battery light. You are way better off going straight to Ford and ordering one, even if its a ford stock reman you will get way better than any garbage Murrays or Autozone reman alternator. Although you might also get lucky...
I specifically remember a night when I headed out to reebs' house to buy some car parts off of him. As I got there my alternator took a crap, he graciously drove me around (in his 3L turbo car! w000t!) to all of the parts places to find a good alternator, we went to 4 different places and tested 4 different alternators while at the parts store, and every one failed right out of the box, until we got to the last one which was a bosch reman that we had no issues with.