Mexico uses the acute accent.
México
Every country has it own accent. Denmark too.
Yes, Cuban Spanish has a unique accent, just as each Spanish-speaking country has its own distinct accent.
Mexico, but without the accent in the 'e'.
Latin America accent
El Zocalo, Ciudad De Mexico by the way there is an accent mark above the 'O' in Zocalo and an accent mark on top of the 'E' in Mexico.
Clasico (with an accent over the'a').
'Mexico' in Spanish is still 'Mexico.' It is pronounced differently, though. It is pronounced, "MAY-hee-co." It is written with an accent, "México", to designate the pronunciation is not "standard". Following normal rules, "Mexico", without a written accent, would be pronounced "meh-HEE-coh".
Yes
The word Mexico does have an accent in Spanish, but not in English. There are no accents in English; the words in which we are used to seeing them (resume, fiancee) are actually words from other languages - usually French - that have been loaned into English. The word "Mexico" looks so similar in Spanish and English that I don't think it matters if you use the accent when writing in English.
On the e: México.