What are the duties of a Vice President?

Everything varies state-by-state. I suppose that a VP can be given responsibilities to handle per state rules, but for most states this is just a title that comes with a buff and nothing more.

Unless your state has a specific duty for the Vice President (very uncommon), then you were probably appointed VP just to take advantage of the Build/Training/Research speed buffs that comes with the title.

Most states have a chat room with most/all of the state's leaders somewhere - which usually exists on a third party app. This is usually known as the state's council. Your council is usually where your state's rules originate from.