YES
A Mexican-American.
The US Congress makes the rules for becoming a US citizen. The House of Representatives and the Senate together decide who can be a citizen and how it is to be done.
No, you are Mexican.
Not legally.
No. Neither will automatically become citizen of the other country.
On becoming a US citizen.
Officials will decide if your criminal background may or may not prevent you from becoming a citizen.
th
Definitley not
no
no
Yes, you apply at the nearest Mexican consulate.