Well, of course no. generally speaking, there is no relation between your tooth and your eyes. So you do not need to worry about it. And even if you have bad tooth, it will just lead to some tooth problems, but not eyes. But on the other hand, according to some researches, if you get a systemic infection from the tooth, it could certainly spread to the eyes. In that way, your eyes will suffer eye infection in some degree. I also have heard that someone who nearly died from a systemic infection due to a mouthful of rotten teeth. Anyway, when you have a bad tooth, just try to treat it, or it may lead to some serious problems.
Yes, the health of your teeth and gums can dramatically affect your vision. I am seeing this more and more in clinic with varying eye conditions, from ocular lymphoma to glaucoma, and retinitis pigmentosa to uveitis. Increasing numbers of people are developing eye conditions that may result from tooth decay, mercury fillings and gum diseases. It's no coincidence that for many, the vision starts to go around the same that the teeth start falling and/or become problematic. There is no way that the fumes from mercury fillings cannot directly impact the health of the brain, eyes and rest of the body. I advise everyone with mercury fillings to consider getting them safely removed.
Yes, it is possible for you to affect the vision due to bad tooth because the teeth nerves and eyes nerves are interlinked at the whole body. You should better protect the teeth health which could also affect your diet. Both teeth and eyes are important for our whole body health. We need to protect them carefully.
It may be the case. As there is a highly density of eneurosis in our face, they are linked to each other, if one organ is not right, others may be affected. The degree of pain should depend on how close they linked with each other. But for my advice, you have to pay attention to that in case of it is not caused by the tooth but an independent symptom instead.
Hope that will help.