Well the fish it ate with the long snout was probably a birdmouth wrasse. Frankly a fish that size I am guessing if you got it from a lfs I bet someone brought it back because it got to big for their tank. This Puff has bad manners and I am afraid at 12 inches it is going to be very hard to change its outlook on its tankmates (as dinner items). If you got it from a lfs you need to get the low down on where it came from and was it brought back for doing what it is now doing in your tank.
Now here is what I see. Anything it can fit in its mouth is going to go there because it obviously is used to live food (that is bad). I would not feed it any more goldfish or live shrimps no matter how sad it is going to look like. The tank size is good and I hope the other fish have places to hide at night as that is when the dirty deed with Puffers is most likely done. The fact it is the biggest fish gives it the edge and it is using it to keep its tummy full. If it ate 6 goldfish today it probably would not eat every day as it has to be very full. Puffers will eat till they are so full they sink to the bottom of the tank for a day or two till the food is digested. So do not overfeed it. My large Male Pork gets 8 to 10 pieces of frozen Krill or a few decent pieces of frozen squid and that is it I don't care how sad those big eyes look he gets what I feed and that is it. The large female is not as aggressive at feeding time but I see she gets her fair share also. Frankly you have a problem here as I don't believe the hawk unless very large will last to long (had one eaten by my large Dog after being in same tank for a few weeks then one day boom (the Dog cornered it as I watched and then started chewing on it). Unless you can get it to feed on frozen foods (krill, squid, large silversides) then you are never going to tame it to be with other fish (that is why my Dogface lives alone he has bad table habits when it comes to tankmates).
I could go on and on but I think you need some background on these Puffs so I suggest go to my homepage (man standing by house) and check out the info available there on Puffs. I am going to think about this a bit and try to figure what you might do to calm this one down but start please by forgetting live food it is only giving this Puff the wrong ideas.