There are plenty of examples of first person narratives by a character whose speaking level isn't easily comprehensible by the reader. The character Benjy Compson in Faulkner's The Sound and the Fury is notoriously difficult to understand, as every sentence is somewhat disconnected from those that come before and after, in both time and space. His brothers, though able to form a consistent narrative, are likewise difficult to understand. Faulkner's As I Lay Dying uses both dialect and intelligence levels in portraying over a dozen first person narrators, and while these do pose a difficulty for the reader, a texture and pattern begins to develop that helps guide the way. Stephen Dedalus, a very careful and articulate thinker in James Joyce's The Portrait of the Artist as a Young Man and Ulysses may also be considered a poor communicator, largely because his obsessions are far beyond those of the average reader, and these inform much of what he is saying. Going much further back in English literature, we have Tristram Shandy, whose communication skills are so poor that, while he can write very well, his autobiography doesn't make it much past his own birth (and for all that, it's a very funny and worthwhile book).
As long as the voice is consistently used, and you the author are aware of what is being left out by the speaker, a compelling story can be told.
As a side note, we have a whole category of narrative technique wrapped up in the "unreliable narrator", someone who tells a story, but is either willfully lying or doesn't know as much as he or she thinks they know.
Regarding differentiating the author and the protagonist. A third person narrator (the author) can insert himself into the text via commentary and asides. Readers often need cues if both the narrator and the protagonist are guiding the text. This is a huge challenge, but if you want to portray the thoughts of the protagonist as separate from the narrator's storytelling, the convention is to italicize the thoughts.