Yes, there are anemones that will eat fish and it is not a good plan to buy such an animal without any idea what it is. Actually it is not good to buy any animal without being able to do research on its needs. Russian Roulette my friend, and you learned the hard way I guess
sorry.
However, the bicolor angel is quite a delicate fish, and many anemones will eat dead fish as well. How about telling us more about the tank...exact water params (ph, specific grav, ammonia, nitrite, nitrate), age of tank, how long you had the angel, etc. And any pics of the anemones, if possible
Oops...I see you list that you have a carpet anemone, a known fish eater, which will get very very large. That is a problem right there. Also, bicolor angels tend to due much better in very mature tanks with loads of LR on which they graze. Without it, survival tends to be pretty low.