I studied quite a bit of Myers-Briggs (and Enneagram, which I like even better), and ideally there are some correlations. Liz Greene directly relates: fire-intuition, earth-sensation, air-thinking, and water-feeeling. I just so happen to be predominately fire and water, and I'm an INFP, though I do havesome air and eath to balance. I've given the Keirsey Tempermant Sorter to about 80 people I know, and more often than not it does correlate to their ntal chart, but not always.
As for E/I, I again like Liz Greene's theory that there is an extraverted and inyroverted version of each sign. Some try to say that some sign have a tendency to be extraverted or introverted, but I think that comes from a skewed version of those definitions. For example, many people assume introversion to mean shyness, when that is not the case. Introverts are merely tired out from small talk, whereas extrzverts don't mind it, but both Es and Is can be afraid to initiate a conversation. This is jst one example of the differences between Es and Is, I'm not trying to define them.
Also keep in mind the turntype. This is someone who may be naturally inclined to be a particular type, but had to develop only their inferior functions due to childhood upbringing in order to survive (usually psychologically, sometimes physically).
Hope that helps!
Matt