I'm no GR expert, but I believe the answer to the thread's title question is 'yes'. Any local observer will observe c to be constant, no matter their frame of reference, but distant observers may not, if their is a difference in gravitational potential between the two. At least, I think that's how it works.

<<As the universe continues to expand, C is slowly changing. The constant, C, is a manifestation of the given space within which light travels (i.e. the whole of the universe as it is). But it has been found that as the universe changes, so too does this constant C (among other things)>>

I don't think this is right; at least, last I heard, no such effect had been observed, or predicted by accepted theory. On a cosmic scale, light does, in a sense, "cover more distance" than it actually "travels" (at speed c), because of the expansion of space--but that doesn't mean c itself is changing.