1. I worked in WA for half the year. Since my employer is not registered in WA, they deducted NJ taxes from my paychecks. What would I need to do to get that tax refund from NJ. I believe I should get all the tax back, as I never worked in NJ? Please explain the process

2. For 2nd half of the year I worked in NC, and NC taxes were deducted from my paychecks. Do I need to file NC state tax?

3. What is the minimum period one has to live in a state, to be liable to pay state taxes for that state?

1. File NJ return. Attach letter from employer that you worked and lived in WA and you did not live and work in NJ.

If you are present in a state, then any income earned during this period, must be reported to the state.
To your resident state, you must report your worldwide income for the year.
If you live and work is a state but your employer is from another state, then your income is only subject to the state where you live and work. Read: Your U.S. Tax Return: Working or Living in Two or More states