Is it normal for babies to hiccup a lot?

Yes. Hiccuping is very normal for newborns and you can expect the frequency to decrease by the time they are a couple months old. Generally the hiccups do not bother your baby and they are not dangerous or causing any damage to your baby. Sometimes feeding or burping your baby can help them go away.
Yes. Newborns and young infants hiccup a lot. Some babies start hiccuping before they're even born and moms will report having felt a rhythmic fetal movement towards the end of pregnancy. Hiccups become less frequent as your baby ages and by a few months it will no longer be a common event.