Mine had them so much too...when she was born she still had them a lot and it was cool to see what it looked like in person...she jerked her body the same way I described it when she was in my belly...so cute...
Nope, it doesn't hurt them and from what I hear it really doesn't bother them much. My little one gets them 3-4 times a day. Once or twice in the afternoon, once in the evening and then again before I go to bed. The hiccups usually last anywhere from 5-15 min. I always tell my lil bugger to stop inhaling that fluid so quickly, but s/he never listens! LOL