If page A links to page B with 3 links (top nav, bottom nav, and in text), does page B gets 3 "votes" and page A counts 3 outbound links, or the number to the outbound links to the same target is irrelevant for both A and B pages?

Only Google knows for sure.
The conventional wisdom is that page rank for a given page is divided up across the links on that page to other pages. Thus, 3 links to one page might get a little more weight to that target page, but at the expense of other links to other pages. This is the whole idea of page rank "flow".

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