CDN on a visitor's visa in the US wanting to do consulting

Hi there, my situation is this: I am currently in the US on a visitor's visa for the 6 months I am legally allowed to be here. I have been offered a project to consult on from a US based company while here, I have an incorporated CDN consulting company registered in Canada.

My questions are this:

(1) Is this situation legal?

(2) If yes to Q 1 then how would I be paid by the US company? By cheque upon invoice?

(3) Am I required to file taxes in both the US and Canada since the source of my payment will be US based in US dollars?

Thank you!

1. Only if you get a work status, like TN (at the border). You are now a visitor, not a worker.
2. Once you get a TN, they can pay you by invoice, if that is what you want
3. Not likely have to pay in US, as long as you do not spend 183 days in any 12-month period in US

Thanks AGN!