Let's say we're in phase 2. Can miners still be placed in a phase 1 corridor?
Also in phase 2, could the players make a chain for the bottom and start opening up a phase 3 corridor or do they have to wait for phase 3 to begin?
Don't see anything in the rules so I assume there's no restriction, but I'd like to be certain.
Yes and yes. Often going for Phase 1 during Phase 2 or 3 during 2 is a different but it can be a rewarding strategy because you rarely have any competition since most want the better salt down below. Not often in fact I've never had anyone wish to go down to 2 or 3 during the previous phase just because of lack of workers. I think once someone thought about it in a 4 player game, but the cost to get any salt out of there with the player's lack of workers was insane so he opted not to attempt it.
I assume the reason the areas are marked I, II, III is simply the salt contained within will benefit you more with the current round's king's demands.