Well, I have a school of 8 tiger barbs in with my cichlid tank and I am pretty sure that they were the ones picking off the fry in the tank as I was running to get my net to rescue them. I dont know how much they are into eating other fish though, but like everyone has said, if it fits into a mouth, then it will probrably end up in one....
Still, the tiger barbs are always going to be prone to nipping fins and I do not think this is a behavior that is brought on by under feeding them. Tiger Barbs get pretty darn big as well so that can be a problem later on since they can nip harder and with larger 'bites'. My 8 tiger barbs have to be over two and a half inches long and at least an inch and a half from top to bottom. They have the same body as the tinfoil barbs or similar to a silver dollar which is weird for me to see since I usually only see them as juvies at a fish store and they have that sort of longer body type.
The good news for you though is that molly fry, and most others, grow VERY fast into something too large for most community fish to get their lips wrapped around. I used to have a 55 gallon livebearer breeding tank and it only took maybe three weeks before I could be relatively confident enough to put them back into my main tank. A breeder's net or box is a good idea since it will ensure that your molly fry are accustomed to the tanks water types and parameters that you have on a regular basis because they are in the tank, but just seperated from the rest of the population.
Also, and this is not to say it is wrong to keep them in freshwater, but to get the maximum lifespan and potential size out of most mollies, a brackish water tank is the best way to go about it. Of course, they are almost always sold in plain old freshwater and then put into a freshwater tank so it isnt a really big issue. They do get a lot bigger in brackish tanks though. I have seen, with my own eyes, a molly live for weeks in a completely saltwater tank and I am sure that they could have lasted longer had I not taken them out (I used them to test my SW tank's cycle to see if it would have a mini-cycle or if the tank was ready for fish to be put in). In fact, I think some people breed the mollies just to have a live food source for saltwater fish since they can last so long in the tank and do not die from being in there before they serve their purpose. Of course, I do not really condone this, but see how it could help out even though feeding freshwater fish to saltwater fish is not really a good idea in the first place.