My two year old has blood in her mucus when her nose runs. Is this normal?

Normal, no. It is not normal for a two year old to have blood anywhere, but this time of year when the air is colder and drier this may occur. Moisturizer the air with humidifier next to the bed and a little cocoa butter inside the nostrils a few times daily. If no improvement, see a doctor.
Dry nose. It may be secondary to a viral cold or a dry nose. Use a saline nasal spray or gel to ease it. If it continues, see your doctor, especially if the discharge is in one nostil, she may have gotten something stuck in her nose.