No unless stopped. Anti seizure medication actually protects against seizures and does not cause seizures. However, if you suddenly stop the medication without taper and have been on it awhile you're at risk of having a seizure. This can happen even if you haven't had a seizure before. That is why it is a good idea to taper the medicine down before stopping it.
No. Caffeine use definitely does not cause either seizures or bd, nor is there a link between seizures and bd. Although a number of anticonvulsants turn out to be effective treatments for bd too, that does not mean that bd is a seizure disorder. Often, classes of medications work for a variety of unrelated disorders.
Possibly. Many with bipolar d/o also have seizure d/os and vice a versa, particulary partial-complex seizures also known as temporo-limbic epilepsy. Caffeine has been known to lower one's seizure threashold making certain seizures more likely and possibly worse. Good question.