Do the fossils say this? Or is this just taken on faith?
Coming to a reasonable conclusion about something is not "taking it on faith". I am not a biologist, nor am I a paleontologist, but I do not have to be one in order to propose a means by which something could have happened. Also, one of the problems with fossils is that most organisms don't last long enough to become fossils to begin with. So it's by nature an incomplete (highly incomplete) record.
But, is that shown by the fossils?
Given that I am not saying that you should accept it just because it's reasonable, I don't see the relevance of continually asking me about the fossils, especially since I'm not in a field that deals with fossils.
Where does the new information come from for the mutations?
From the environment, since mutations are caused by environmental factors.