Common. The face of infants is often in contact with clothing and blankets and spit up. All these things can couse minor rashes on the face. Use a wash cloth frequently it helps. If it is very severe see your doctor there are medicines but we try to use them sparingly.
Bumps on 1month baby. It is difficult to answer without a better description of the bumps or a photo of babies face. It could be infant acne, and that goes away by itself, or it may be seborrhic dermatitis. Do not put any steroid cream or lotions etc. If still concerned see yor pediatrician. If she does not have cradle cap and rash is limited to the face, I would suspect it is acne, which in babies do not need any therapy.