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....
Wanna calculate the cost of that new reef tank?? Take your worst nightmare, double it, and you're halfway there.