Does anyone have an intimate knowledge of the process of applying for a residency position in the states? In particular, who do you request letters of recommendation from besides the Dean? Is it crucial to develop a professional relationship with the faculty while undertaking BMS in the Caribbean?

You will require 3-4 LORs from faculty in addition to your dean's letter. This does therefore require a professional relationship with some medical school faculty so that they feel comfortable writing you a letter; letters are generally from clinical faculty you encounter in the 3rd and 4th years of medical school.

The details on applying for a US residency as an IMG have been detailed here endlessly. If you can't find sufficient info after a search in these forums, check http://www.ecfmg.org for more details.