Is dizziness common in pregnancy?

Yes. It's very common. Tell your doctor, so you can rule out dangerous conditionns. Try drinking lots of water and eat regular meals.
Yes. Pregnancy is associated with stressors. The brain regions that cause dizziness can be affected by blood pressure changes, and by fluid changes, and by hormone changes. Some women start to get migraine symptoms when pregnant that can produce severe dizziness. Discuss with your doctor to be sure more serious problems are not present.