Looking for an ID for someone. Lots of hair algae but what are the toad stool looking things. Close up almost looks like some kind of macro algae. But not sure.
If your tank is large enough and the other inhabitants are compatible, a small tang like a Yellowed Eye Kole Tang (there are several types of tangs) as well as a Fox Face will clear up both of your issues given some time. If not..... You'll want to remove the Caulerpa completely as fast as you see it, as for the hair algea an emerald crab will make quick work with that.
If you go the fish route keep in mind that you'll need to provide Nori strips once they have cleared off the algae along with what ever else your feeding.
I have some emeralds, a Foxface and a Kole Tang, between that trio of algae eating machines they were completely hiding a nutrient issue that I was having when I got sick and didn't test for two weeks.