My newborn has a rash that looks like little pimples or freckles; will it go away?

Yes. As long as your baby is healthy (no fever, feeding well, and you do not have a history of any significant infections during your pregnancy), it is likely this is a benign newborn rash. The most common after birth are (1) erythema toxicum- minor rash that looks like flea bites and fades in the fist 1-2 weeks after birth, and (2) baby acne- appears around a month, resolves spontaneously.
Yes. These rashes are common in newborns. The most common one peaks at 5 weeks of age and is gone by 2 months of age. These rashes tend not to itch. For a pimply rash that itches or is present after 2 months of age, contact your child's healthcare provider.