Question

What is going on in the hexane layer at the end of the Group I anion experiment?
(when color of hexane layer is yellow you have Br- and when it is brown or purple you have I-.) please explain
This question is too vague for me to answer. I don't know what you are looking for in an answer. Perhaps something about Dispersion forces (instantaneous dipole-induced dipole) which is responsible for the violet color (and for the yellow color of the Br^-). By the way, I wouldn't expect a brownish color to indicate iodine unless the hexane layer was contaminated with some water or alcohol.

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