1) Read all of the following couple times......it could be considered a second home for the Mortgage interest deduction, but read the whole article about what facilities it must have in it. The article deals with mostly as a primary home, but also the "second home" is mentioned in the next-to-last paragraph.
https://blog.turbotax.intuit.com/tax-deductions-and-credits-2/home/can-my-boat-or-rv-be-claimed-as-a...
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2) No...utilities and rental fees cannot be used...those are just living expenses.
3) A tax filing for the other state would be required....for her, whether that would be as a as a resident of that state, or as a non-resident depends on the situation and whether it is a job expected to last more than one year. Sometimes that can be done on a MFJ tax return, and sometimes not. And that gets far more complicated. IF she can arrange to be in your primary home more than 183 nights during the year, then perhaps filing the other state as a non-resident would work (Fri Sat, Sun nights in your current home...plus all holidays and all vacations and time off....plus, perhaps some telecommuting if they allow it.) But if the employer also requires her to have an in-state driver's license (and other proofs of residency), or if she ends up staying in the other state more than 183 nights in the year on a permanent basis...it gets more complicated.
____________*Answers are correct to the best of my knowledge when posted, but should not be considered to be legal or official tax advice.*
