Probably. States tax residents on worldwide income, just like the federal government. Residency is broadly defined in most states as spending a number of days in a state. Visa status does not impact state residency.
There are generally no tax treaty arrangements between individual U.S. states and sovereign nations.
The Rental property is in the UK, its a home i left behind and now rent it out, i dont mind paying tax to the State but Turbo Tax is asking me the question and i dont know :(
it depends. To clarify, what state are you working on and what questions is it asking?