A murder is caught on TV and taped. The killer is clearly identifiable. Does he/she still enjoy the presumption of innocence? How and why?

The court will require to establish that the evidence is admissable and make formal confirmation of the identity of the person in question. 

It might help to think of "presumption of innocence" as a category that people who are suspected of committing a crime are placed until they are officially declared either "not guilty" or "guilty" by a court of law.

Since a defendant is "presumed innocent" (the category), he has certain rights that proceed from being in that category, to wit:

Due to the presumption of innocence, a person cannot be compelled to confess guilt or give evidence against him/herself. It is for the state to produce evidence of guilt, not for the defendant to prove innocence. In general, therefore, a suspect’s silence should not be used as evidence of guilt.