1) Should I be receiving anything from state #2 even though I did not receive a refund?============>when you receive a refund of state income tax, that amount appears in box 2 of the 1099-G form. However, you don't necessarily have to report this amount on your federal tax return or pay additional federal taxes;for state #2. You may receive a notice showing a penalty for Failure to Pay the Tax Shown on a Return by the Due Date, you were charged an underpayment penalty for not paying your taxes by the April due date. You may contact state #2 dept of revenue for more info in detail.
2) Am I able to account for the offset from state #2 when calculating the taxes I owe from deducting too many state taxes on my 2017 return?=============UNLESS there is a reciprocal agreement between the states and your home state, you need to pay taxes to state #1 and #2 as a non resident of state #1 and #2 and claim tax credits on your home state return on the state tax that you paid to state #1 and state #2. Also on your federal return, I mean on your 1040, if you itemize your deductions on SC\ch A of 1040 then you may claim state tax that you paid to your home state on your 1040.