If they are being feed or there is lots to scavenge, they will grow faster and molt faster. While they do need proper trace element amounts to build their new skeleton, just doing water changes is more than enough to supply them with the elements they need for proper molting.
I dont often do water changes, but my shrimp still molt every 3ish weeks.
For your shrimp, i wouldnt worry about testing or dosing iodine. But it wont hurt to have the test, at some point if you have lots of fast growing SPS corals you might find it to be one of those things you need to test and dose for.