I live in California and will be starting work at a hospital. There are many people who speak Spanish and are from Mexico, I speak Spanish, but I find this accent to be the hardest to understand. I am looking to travel in Latin America to improve my understanding of the different Spanish accents so I can assist those who speak at the hospital where I work.

I was at a party, making small-chat with a girl from Venezuela, and she said that she can understand most Spanish accents but can't understand a thick Mexican accent?

What is a Mexican accent anyway, and what makes it so different from, say, a Colombian accent that others don't understand it?

I was wondering what are the main differences between all the Spanish accents.
I am trying to learn Mexican Spanish...but what is the differences between Mexican Spanish (Español mexicano), Latin American Spanish (Español latinoamericano), and European Spanish (Español europeo)?

When traveling in Mexico, I smile when I meet a Mexican National with perfect non-accented English. In contrast, I still meet American-born Hispanics with heavy Spanish accents. Someone told me that learning English at an early age (even as a second language) breaks that accent carryover. Is that true?