Sounds like diatoms, which would be pretty normal for a new tank. Dusty brown = diatoms. Slimy brownish-red = cyano
, and is a very bad and NOT normal thing. But I'm thinking it's probably diatoms.
Give it time and it will burn itself out. I'd normally suggest a cleanup crew of snails to eat it up for you, but I'm afraid your Trigger would make a snack of them.
Seems like a lot of fish in the tank already for just one month. Tank was cycled... right?
Coralline on live rock will take a while, and depends a lot on your calcium/alkalinity numbers. But I'd say 4-6 months and you should see some good growth.
Welcome to Aquarium Advice, by the way!
(P.S. This section of the forum is where folks normally post their "New Acquisitions" as in "... things I'm showing off that are new to me." I know the algae is new to you (!) but that's not really what people look for here. Plus this area doesn't get much traffic. You might get more feedback from folks if you post in the "Reef Aquaria", "FOWLR
", or "Getting Started" sections. Those seem to be the well-traveled areas of the site.)