That one is more complicated. In short, yes but you'll get a credit towards NJ state taxes so you aren't actually 'double taxed.' Have to file a return in both states and the math for calculating what you owe is a bit weird but it basically works out to be similar to working in only one state for most people since the NJ versus NY rates are similar enough.

Yes, but NJ taxes are roughly the same as NYS taxes (actually a smidge more in most brackets, but JC/Hoboken offers SIGNIFICANTLY better infrastructure than Long Island or Westchester)

It’s the city taxes that make the most difference