1. I understand that on your W2 there was WV withholding but zero KY withholding so assuming none of your self-employment was performed in WV then, yes, you will file the special nonresident WV return. If some of your self-employment was WV source then you will have to file the full nonresident WV return and pay WV taxes on the WV source income.
2. You are correct KY will not give a credit for taxes paid on salaries/wage income to WV as part of the reciprocal tax agreement. Further, you will be getting all the WV withholding back so no taxes paid there. If you paid WV taxes on part of the self-employment you could claim a KY credit for that.
3. You will input the forms 1099-NEC in the federal interview and KY will automatically tax you as your resident state on that income (whether or not you put KY in the state boxes).
4. The timing of your payment to KY is your choice. You can file all the returns when ready. You could then wait until the deadline (18 Apr) to pay KY with anticipation that your WV refund will be deposited prior to that. Yes, there may be KY penalties for underpayment depending on the size of the KY tax owed.
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