The worm-looking "parasites" are some variety of fire/bristle worm. They're largely beneficial detrivores that can sometimes cause problems, but 95% of the time they should just be left alone.
The anemones are aiptasia anemones, nasty little hitchhikers that can grow to plague proportions and crowd out anything else. Very hard to take down once they get established, most successful long-term tanks include animals specifically to predate on aiptasia. More on that in a second.
The algae looks like it could be bryopsis. It's a stubborn hair algae, made worse by the fact that most CUC won't eat it. There are a few creatures that will, but depending on what you have in your tank already there is a relatively simple treatment for it. Said treatment (Reef Flux) is not without its downsides, so don't just rush out and get some.
What size is your tank? How long has it been running? Do you have any corals beyond zoanthids and mushrooms?
As far as aiptasia goes - there are a range of things you can do to get rid of aiptasia. None of them succeed 100%, which is why long-term control usually involves some variety of aiptasia predator.
First, there are chemical treatments. This usually only works when there are just a few aiptasia present. Take a solution of some variety (kalk paste is my favorite, but there are other solutions that work) and smother the disc of the anemone in your solution. Alternately, pierce the body of the anemone and inject directly. This works to kill the anemone, but the problem is that one of their survival mechanisms is to release larvae when attacked. So if you don't kill it fast enough your one anemone becomes hundreds of anemones.
Second there are physical treatments. Things like hydrogen peroxide, superglue, UV torches, lasers, etc. These mostly have the same problem: If they don't kill fast enough, then the anemones can multiply and spread. Additionally, both chemical and physical treatments share the problem that they're relatively time-consuming to apply. If you have a large infestation, it can take hours to treat every aiptasia.
Finally, there are biological treatments. Bringing in something to eat the aiptasia. There are fish that will do so - Australian Stripey, some butterflyfish (most notably, copper-banded butterflies), bristletail filefish. There are also some invertebrates that will do so: Kukenthal's shrimp, certain species of peppermint shrimp, Berghia nudibranches. But there are problems with all of these as well, ranging from coral predation (most fish that will eat aiptasia will also eat corals), ineffectiveness (most shrimp that will eat aiptasia would rather eat other things) or obligate predation (Berghia only eat aiptasia, which sounds great until you realize that your population of Berghia will starve to death, usually before they completely eliminate aiptasia).
Controlling aiptasia is a complicated and never-ending problem in the hobby.
