[A Single C in Masters, how will this affect me?]

You definitely shouldn't mention it if you are trying to explain why it's unjust. That will probably make it seem like you're making excuses. But do explain if there were any extenuating circumstances on your behalf.

[Need Advice: Grad Admissions from non-Phil background]

Agreed with the above. That's strange policy on behalf of your department, but you can try to make do with recommendations from others professors/mentors/peers. I've met people with online degrees who were admitted into MA programs, so it's not out of the question, especially if you've been doing well in your classes. Your main goal should be to have a solid writing sample, and a statement of purpose that explains your situation as well as your aptitude for continued study of philosophy.

[Got a C+ in Intro to Symbolic Logic: am I doomed? (And should I mention it in my personal statement if not?)]

It's not the best but it's not the worst, either. The fact that it was only in your sophomore year helps a bit. Perhaps best not to mention it, but get some second opinions from professors. Is it too late to take it again, or enroll in a similar course? That's something you could mention.