Taxable scholarship - tax implications for federal and NJ state

My child resides in NJ (I claim them as a dependent and I live in NJ).  They attend a college in NY full time.  

Their income on their W2 (from a job in the summer) was $5665 (no federal or state tax withholdings).  They received scholarships that covered all of their tuition and also covered their room and board, which was $7990.  On the 1098-T, Box 5 - Box 1 equals $9557.  They have $814 in "other educational expenses".

My questions are:

  • Do they need to file a federal tax return if the amount is under the federal standard deduction?
  • Do they need to file a NJ state tax return?
  • Since I don't receive an education credit for them, would it make more sense for them to file separately (as a non-dependent)?  Is seems like we would save around $250, if I removed them as a dependent and they filed separately.  I just don't understand the implications of doing that (are they now a resident of NY, do they have to pay NY tax AND NJ tax then?)

Thanks!