I don't believe you'd be able to apply for asylum at the border, as you're already in the states, because of the Safe Third Country Agreement unless you meet certain criteria:

There are four types of exceptions:

• Family member exceptions

• Unaccompanied minors exception

• Document holder exceptions

• Public interest exceptions

That said, I am not a lawyer and you should consult a lawyer about asylum claims as they are generally beyond on the scope of the sub.

As for your final question: the immigration pathways available to Americans are the same as everyone else, with the added possibility of a NAFTA/CUSMA work permit. As long as their spouse is eligible/admissible, the spouse could accompany them, yes.