For the anemone, you're going to want to feed it slightly larger food than brine or mysis. Silversides are a very popular choice, and you can usually buy them frozen at your LFS. I've also used fish (tuna, Mahi, grouper and others), shrimp, krill, clams, and just about any other type of seafood I get my hands on. I like to keep the pieces no bigger than half the length of the anemone's mouth.
The Euphyllia (hammer coral) I've had a difficult time getting to eat, but mine has been fine without any direct feedings. Zoanthids seem to be a little hit or miss on what to feed them and how likely they are to take it. As Snowman said, though, I wouldn't worry about feeding the zoanthids directly.