Chloride (note - not chlorine!) competes with the nitrite for take up at the gills, so it's taken up instead of nitrite. I'm not aware of it having any effect on chlorine poisoning, since chlorine is not ionic so can't use the same uptake mechanism.
Get the basic tests, but also get GH and KH. Mollies cannot (IME) live long term in soft water, so you need to know the hardness.