"I live in Mexico."
Translation:Vivo en México.
Yes "vivo" already implies "yo vivo" so the yo can be left out, unless you want to emphasize it is "yo"
Is this because the "vivo" form can only be used with 'tu' so it's just a shortcut?
Don't know if this answers, but the accent in Mexicano is on the a, where it would normally be, so an accent sign isn't needed. In general, a word ending with a vowel is accented on the next to the last syllable. The word México doesn't follow the rule, and the accent needs to be marked. But that may not be what you meant to ask. Maybe you meant to ask why México is pronounced with the accent on the e. I don't know.
Mexico is pronounced incorrectly. The "x" should make the "j" sound in Spanish (like the "h" sound in English).
Please read the responses that StefanMerrison got when they asked this question.