Should I be worried that my newborn crosses her eyes?

How severe? If she briefly crosses her eye, but they usually are "straight", monitor the frequency and duration and discuss it with your pediatrician on the next visit. If they are perpetually crossed, i would have her seen by a pediatric ophthalmologist.
No. Infants have an immature nervous system and can have intermittent eye crossing during the first few months of life. As they age this matures and between 2-4 months of life you should no longer be seeing any eye crossing. If the eye crossing is still seen after 4 months, or if it's persistent in the first 4 months, let your pediatrician know immediately.
No. Newborns will cross their eyes usually up until 2 months of age.
No. It is not unusual to see babies cross their eyes frequently for 2-3 months after birth. Not only does the visual part of their brain have to mature, but their eyes are controlled by muscles that have to be trained as well. However, if one or both eyes appear to be locked in one direction all the time, see your pediatrician.
No. New babies often have disconjugate gaze (the eyes don't look in the same direction), especially if they are not trying to look at anything. The gaze should straighten out over the first 3 months, but parents should let the doctor know at the 2-week, 1-month, & 2-month check-ups about the gaze. Babies with disconjugate gaze after 3 months, or who have additional symptoms, should see an eye doctor.