Short answer to 1. Yes. Short answer to 2. No. Start of long answer to 2. No but if it is a small amount and depending on how the tax withholding forms are filled out, there may or may not be state and or local taxes withheld. Location of the work performed governs. i,e,, construction workers from Ohio working on a project in Indiana get Indiana taxes withheld on those wages (or should) New Jersey resident working in Manhattan gets NYC and state taxes withheld. Have to file non resident tax returns in those non resident state(s), to pay additonal taxes or receive refunds. If income is high enough, (varies by jurisdiction), return is to be filed regardless of whether tax is owed or not. However, you will always have to file to get a refund. They won't automatically send it to you. You can receive a credit on your resident state return for taxes paid to other states as well. Again, the methodology changes from state to state. You generally do the the returns for the non resident states first, so you have the actual tax paid to them so you can use the correct amount to claim on your resident return.
Happy tax season.