No your home office would not be considered a Bona-fide employer location.
Yes NY will be able to tax your income.
Yes you will be able to file as a Non-Resident of NY to receive credit for the withholding on your Virginia return
New York state is one of those states with strict filing requirements for Non-Residents.
You will need to file a nonresident return for NY if there is NY withholding on your W-2. If you are filing a resident return for Virginia, you will be given a credit for the amount of tax you must pay on this telecommuting income to the other state.
Use the links below for further guidance on these issues:
How to Enter NY income as a Non-Resident
NY Department of Tax on Non-Residents
NY State Non-Resident Workers
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