Is it normal for my newborn to be losing weight?

Depends. You didn't mention how many days old the baby is. Babies can lose weight in the first 7 days of life, then should get back to birth weight by two weeks. At this point baby should be gaining a half ounce to an ounce daily. Hope this helps!
Yes. Newborns are born with extra water and in the first week almost all experience a weight loss as they lose this extra water. As your milk comes in and your baby begins to eat more s/he will regain this weight and begin to gain 20-30 grams a day. It is normal for a newborn to lose up to 10% of their birthweight. We expect babies to be back at their birthweight by 2 weeks of age.
Yes. Most newborns will lose weight initially. Babies are born with some extra fluid weight, probably to prepare them for the transition when breast milk is low volume at first. They will typically lose some of that weight at first - even formula-fed babies will. We like to see them regain their birth weight by at least 2 weeks of age.