Chicks can die from all sorts of things. I'm not sure how long your chick was in its egg before your sister helped it, but I don't intervene until they haven't made progress for 24 hours or more from their first pip. How exactly did your sister help the chick hatch? It's important that you stop once you spot blood when you are helping a chick hatch. If you see a good amount of blood, you should put cornstarch, blood stop powder or flour on the blood and place the egg back in the incubator/broody. Did the chick absorb its yolk sac?
As far as raising chicks, if you are raising them and not a broody hen, then you will need to put them in a small enclosure called a brooder. A brooder can be made of all sorts of things. I use a cage as mine. A heat lamp will also need to be added to the brooder to keep the chicks warm. The chicks have different temperature requirements as they age. A general rule of thumb is to subtract 5 degrees per week of age. (ie: A one week old chick should be kept at 95 degrees, 2 week old chick- 90 degrees, 3 week old chick-85 degrees and so on.) Once they are fully feathered and the temperature they require is the same as the outside temperature, they no longer need a heat lamp. If a broody is raising the chicks, then she will take care of all that.
Chicks should eat chick starter crumbles until they reach laying age when they should be switched to layer pellets. They can also be raised on flock raiser as well.
Chicks should have some sort of bedding in their brooder (preferably pine shavings). Never use cedar shavings or newspaper as bedding. You should clean their brooder on a weekly basis (remove old bedding and add new bedding, clean feeder and waterer, clean or add a new roosting bar.).