Did you buy this fern like plant, or did it grow out of some live rock ?
Looks a bit like Bryopsis to me, but not sure from the pic.
Bryopsis sp. algae - Photo by John Rice
I also agree that the red stuff is cynobacteria.
It's pretty common for cyno to grow on algaes - I get it now and then in my refugium - but it always goes away.
Cyno being a bacteria - likes nutrients and some light - sort of like our true algaes, and produce/exchange gasses.
I would not worry to much unless the cyno starts spreading around the tank - otherwise I'll bet it eventually goes away if your water conditions are good.