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Can an ic join a unit during any phase other than movement? Say during shooting (eldar battlefocus lets them move after movement phase) or during consolidation after an assault?

Is the only requirement to be part of a unit being close enough?

AFAIK joining a unit is only at the end of the moving phase you don't even need to declare it, if your IC ends within coherency of another unit it automatically joins

ICs can only join or leave units during the movement phase. In any other phase, like running in the shooting phase, or consilidating after an assault, they must remain a certain distance away from other models. It's either 1 or 2 inches, I don't have the BRB in front of me so I'm not sure exactly how far.

Read the section governing IC's in your Rulebook. It explains it in detail of how to attach.