That nem isn't looking too good, but you did just move him..... what kind of lights on that tank?
Bottom left pic - at the top of the pic, I see what looks like the stalk of a vermetid snail... they are a stationary snail that exude a web looking mucus to capture food. Could be what you're seeing..... They aren't bad in moderation, but it you get a bunch of them around a coral, the mucus can damage the coral. If I see a group of them, I'll just take a pair of tweezers and crush a bunch of them at the base.... my six-line loves the extra snack.
The red dots in the lower right appear as though you may have the beginnings of some coralline growth....