A lot of your questions are probably best directed towards your payroll department, who have no doubt done this sort of thing before. But I can answer about the cross-border banking question.
Of the "Big Five" Canadian banks, the one with the largest presence in the U.S. is almost certainly TD. ("TD" stands for "Toronto Dominion", after all.) TD Canada Trust, the Canadian version of the bank, seems to offer a range of services for cross-border banking. I would recommend calling the Canadian bank and asking what they can do for you. Trying to get things set up from the U.S. side is likely to lead to frustration; Canadians needing to do financial stuff in the U.S. is much, much more common than Americans needing to do financial stuff in Canada, and the bank staff on each side of the border will probably be proportionately helpful.