If you live in or near New Jersey, you can visit the Archives and get the copies yourself, without proving a relationship. If you don't live nearby, you can hire someone (or find a willing volunteer) to obtain the copies for you.
I live in Michigan, so a personal visit was not easy. I hired a researcher to retrieve the documents. The cost was less than ordering them through NJ Health, and I have the cause of death.
To my knowledge, arriving immigrants were not photographed. If your family was naturalized in the 20th century, the naturalization paperwork MAY have a photo.