What is the origin of the | (pipe symbol) in typesetting?
That is called the pipe.
Robert Bringhurst tells us:
One use of the pipe symbol in typesetting is for the (usually fifth) footnote at the bottom of a page. In this case, it is doubled and called parallels (||).
Talking of the asterisk and dagger, typographers Hoefler & Frere-Jones say:
See some examples in my answer to this question.