Usually not. Wisdom teeth usually cause problems at the sight of the tooth.
Possibly. Dizziness and headaches may be associated with wisdom teeth, however many other conditions can also cause dizziness and headaches. See your doctor. After obtaining a complete history and physical exam, your doctor may refer you to an oral surgeon, order tests, and/or refer you to a neurologist. Antibiotics may be needed if there is any infection near the wisdom tooth.
Unlikely. Unlikely. Best advice is to see an oral surgeon who can examine you and make recommendations.
No. Yes. Dizziness in my experience is not a common symptom associated with erupting wisdom teeth. Headaches could be. The most common symptom associated with the eruption of third molars is pain at the eruption site. Most people do not have room for wisdom teeth to fully erupt and function. Only about 10% of the patients i see should keep their wisdom teeth. See your dentist to determine if you need help.