Most all fish that dont host anemones wont go near one. Although thats not saying an anemone wont capitalize on a meal should a wary fish happen to get lazy an end up in its tenticles.
All anemones should be considered fish eaters however there are some that have a worse reputation than others. If you want your anem to grow quickly then feed it frequently, every 2 days or so. If you want it grow slower then once a week is fine.
As far as what to feed it, anything raw, natural and fish. Shrimp, clams, slilver sides, mysis etc... varying the diet is a good idea and the portion should be no larger than the animals mouth.