They're not actually pulling out their fluff, they're just grooming themselves. The fluff comes out as the feathers come in and yes, it's perfectly normal. Chicks feather up REALLY fast at first. By 14 days or so their wings will probably be all feathered out and they might even be growing feathers on their shoulders.
The running away in panic is also perfectly normal and the best way to bring them round is probably to wait till they're a few weeks old and start feeding them treats. Food is a great training tool! Keep handling them in the meantime but don't rush to feed them treats. In my experience baby chicks do best on a basic diet of chick crumbles and water and nothing else, at least for the first couple of weeks. If you fill them up with too many treats, they sometimes ignore their crumbles, and then they can miss out on vital nutrition. Loads of people do feed treats from when they're very young and don't have any problems, I'm just mentioning it to be on the safe side.
Personally I find that chicks go through a panicky flighty phase from maybe 2-6 weeks old no matter what I do with them or how much I handle them. Now I tend to handle them a bit but not too much, and wait till they're past the blind terror stage to get them friendly with me. And of course some breeds are a lot calmer and friendlier than others...