If Mexican nationals apply for US citizenship they might get legal papers, IF they are accepted as US citizens.
You are both Mexican and American, as both countries allow for dual citizenship.
There is no procedure. There are ways... get married to US Citizen, get company to sponser you and then apply for citizenship... sorry no procedure.
Both community property rights as well as extended US citizenship to Mexicans in the newly acquired territories.
It is not illegal for Mexicans to come into the US. It is illegal for them to do it in an illegal way. You don't just cross a border, buy falsified documentation, have kids, and assume that everything will be ok and you will become a citizen. We Don't have open borders, with citizenship open to all who can figure out how to cross the border. But anyone from Mexico is welcome to come to the US legally and to work toward citizenship. We are a nation created by immigrants.
True. It didn't happen due to racism and xenophobia: Americans weren't interested in granting citizenship to 6 million Mexicans after the war; instead they acquired the disputed territories which only had 30-50,000 Mexicans.
The right to vote is guaranteed for all US citizens. So they would apply for US citizenship, then register to vote, like the rest of us citizens. Unless you mean getting the right to vote in Mexico.
Mexicans
If you apply for citizenship in another country your US citizenship is automatically revoked. The US does not recognize dual citizenship. You revoke it in writing at a US embassy, outside the US.
Yes, The residents of US territories have US citizenship
Dual citizenship or dual nationality is allowed in the UK. This means you can be a British citizen and also a citizen of another country. Not every country will grant dual citizenship.
The US recognizes dual citizenship.