Well, you have a couple of issues here. First off, your angel is not likely having its fins eaten because a fish is hungry. You have quite a few territorial species in a rather small space, so
IMO you are seeing some territorial nature come out. Your tank is too small for a red tailed shark, and might well be too small for those new cichlids and your unnamed "small cichlid" as well. Do not feed them more to fix the problem. If anything, that will make issues for your angel worse because the water will get dirty faster can the angel will have to fight harder to get it's fins back.
Now, either a fish is harassing your angel at night and biting its fins, or else the angel is unwell and fin rot or some such thing is destroying them. Angel fins do not tend to stay pretty when the angel is too stressed. I think somebody is nipping at them though. Since it is at night, your shark is a prime suspect. However, since you added new fish, they are suspects as well.
To help offer suggestions to fix the situation, could you please get us some pictures of the cichlids, and also of the angel's fins? In addition, do you know your water parameters like the ammonia level? Clean water will help the angel heal faster. I would not treat the tank yet until you have an idea of what is going on. Those sounds like some cool species and we would love to help you out to make a tank where every inhabitant is happy.