Alright so the red sounds like coralline to me, as long as it doesn't look like slime, hopefully someone else can pitch in on what they think.
Ya the plant is aiptasia, which is a type of anemone. The problem with it (other than looking pretty ugly) is it grows like a weed, and will sting EVERYTHING in your tank. Keep treating it until it is all gone, if there is even a little bit left, it will come back. Do not try to rip it out, as if there is a bit of the foot still on the rock, or if a bit of it falls off when you rip it out, it will grow back, possibly even more. If the rock is really small, you could just take out the rock.
I've fought aiptasia a lot. I've tried everything from an $800 class iv laser to an electric probe and everything in between. I've had luck with shrimp eating the small ones and the wand for the bigger ones. I got rid of them all.