The web link in my previous answer will take you to the NY website where you can find the detailed info on both your questions.
Basically your NY-source income consists of:
1. the income you earn on the days you physically work in NY, plus
2. the income you earn when you work remotely from NJ by your own choice.
Income you earn when you work remotely from NJ because your employer requires you to do so is not NY-source income.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
