The New Jersey Division of Taxation says that it takes a minimum of 4 weeks to process an e-filed return, and a minimum of 12 weeks to process a paper return. This applies to all New Jersey tax returns, whether they are filed with TurboTax or any other way. You can check the status of your New Jersey refund at the following link.
https://www16.state.nj.us/TYTR_TGI_INQ/jsp/prompt.jsp
Depends . Sometimes fast sometimes slow. This year i filed it on Monday April 15 and the IRS sent a bank wire today (thurs april 18) that is currently “pending” on my bank statement. This was the fastest as it usually takes me one week to get my federal and usually a week later the state return comes. However I see some people waiting months for their return( that sucks) . Good luck.