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When you place the part tapes on the double-sided tape on the table surface do these tapes need to be accurately aligned (i.e. exactly horizontal or exactly vertical)? Is there only one setup required per tape? I'm guessing that the camera finds the other parts in that tape once the #1 part in the tape has been specified?

The camera looks for the holes of the tape. This way, you need to set up video processing parameters for only three cases (white paper tape, black plastic and clear plastic). You also setup the tape locations When you change the tape, you don't need to be very accurate; just get it approximately in place, the vision will then measure the exact location. Approximate alignment is fine, too; the measurement takes the first and last hole and figures out the alignment.