Fainting and  Dizziness
I have been having fainting spells and dizziness

Dizziness is common in pregnancy, but fainting is certainly not so. The reason for dizziness could be either reduced blood circulation or low blood sugar.  

What does dizziness have to do with blood circulation

In the first trimester your blood supply may be inadequate to fill the expanding circulatory system. In the second trimester, it is caused by the pressure of the expanding uterus on maternal blood vessels.  If it occurs on rising from a prone position, it is called postural hypertension. When your blood pressure drops rapidly, the blood moves away from the brain. In such cases you must get up slowly. No fast jerky movements. Fortunately though, the blood flow to your brain is reduced only temporarily, and therefore will not harm your baby.  

Could staying hungry for long periods result in dizziness

Sometimes it happens when blood sugar is low, and when you have not eaten something after a long interval. So always carry some whole wheat biscuits or breadsticks for such emergencies. If you are in a crowded stuffy room, try to get some air. If you suddenly feel faint, increase the circulation to the brain by lying down or putting your head between your knees