yes you can, plenty of people do that especially at the border.
does a citizen of Mexico need a passport to go from the us to Mexico and back? He is legal to be in us but not a us citizen.
NOPE
A US Citizen would need a work permit to live and work permanently in the UK.
Since your dad is a citizen, I think you are too. You will need to prove it since you were born in Mexico.
She would need a UK work visa.
You can travel to Canada from the US only if you are a permanent resident of the US. Both American and Canadian customs will ask for your green card.
Yes a Zambian citizen can marry a Us citizen and work in the us because the zambian citizen can obtain a citizenship by marriage and automatically become a citizen of us and is allowed and qualified to work there.
You just look for your residence. Both the US and Mexico have a treaty allowing bi-nationality.
Just a work visa
Yes, you apply for divorce in the jurisdiction you currently live in.
no
Yes he can.