In answer to your first question, the chloride helps the kidneys remove bromide out of your body, which is where you want it--gone, finito, sayonara, audios.
Iodine just displaces it, chloride moves it out.
In answer to your second question, as long as you are using unrefined Sea Salt , then none of the myths that you hear about salt should apply. I think some people experience bloating or water retention with their periods, and that is probably where that recommendation comes from. I would think that would be less likely to happen with unrefined salt.