Start at the closest Mexican consulate or embassy.
I may be wrong, but all you need is an I-94 form and your Mexican passport as ID
You'll need a US PASSPORT to return to the US.
Yes, you apply at the nearest Mexican consulate.
You must move to Mexico with your spouse and live there for two years with an immigrant visa, then you can apply for Mexican citizenship. You can have both a Mexican and a US passport and be a dual citizen. If you were not married to a Mexican citizen, you would have to live there for four years.
You go to your Mexican Consulate found in your residing state and there you can call to make an appointment and get your passport and matricula. In the related links section there is a list of Consulates int he U.S.
In the US? No, a passport is the only Mexican document recognized as ID outside of Mexico.
No; you also need a visa issued by the US government.
Indeed.
Just the passport and you're good to go.
Yes. There is no citizenship requirement for marriage in the US. A foreign passport should be enough for you to obtain a marriage license in any of the 50 US states. Showing a matricula consular with a US address may be a bad idea.
"Rejected"
Most foreigners can obtain a Mexican passport if they move to Mexico with an immigrant visa and live there for four years (2 years if married to a Mexican citizen). Then one can apply for Mexican citizenship and passport.