1. The answer is No. Canadian citizens are not allowed to stay in the US indefinitely. They are allowed to come in without visas for most things except E-2.
2. Yes of course.
3. The answer is No but NAFTA visa also known as a TN visa is very difficult if you already have a green card pending or your spouse is a US green card holder. I think what makes sense is probably a H-1 or L-1 type of visa which is not subject to the problems that are normally associated with the filing of a green card or they can wait outside for the green card to be processed. They may be allowed in as long as they are completely upfront about it. When you come to the border as a Canadian citizen and you are going to visit your spouse who is a green card holder you should tell them that's what you are going for. You should not say you are going just for a casual visit.