Yes. I have seen vertigo show up from a dental infection before, but very rarely and typically only in severe cases.
Yes. The ear controls your sense of balance as well as hearing. The inner ear contains a small fluid-filled structure called the labyrinth, which helps the brain find your center of balance. Damage or an infection to this area can cause dizziness or vertigo. In some cases, an infection in the teeth can spread to the nerves of the ears, leading to lightheadedness. Read more: http://www.Livestrong.Com/a.
Possible but rare. I've seen vertigo in a few patients from dental infection but it's rare.