If you do a search on www.familysearch.org for the name Carmine DeLorenzo you will find a lot of entries. The 1905 NY Census shows a Carmine DeLorenzo lived on Mulberry St., and then when you look at the 1898 immigration record it looks like this person lived on Mulberry St. There are also some naturalization records listed.
Try looking for the other names on www.familysearch.org. It is free.
I'm not related to this family but I like helping people out. Many people helped me along the way.
Good luck and enjoy searching and looking at these leads. Let me know if you need any help.
I found what could be Antonio on the Ellis Island website traveling with his wife Anna. It has some handwriting that says he is returning to the US, had resided in US over 5 years. His nearest relative or friend listed is R. M. Piani. It looks like he knows the two parties on the manifest above him because they also show R. M. Piani as the nearest friend or relative.
There are several ship records on the Ellis Island website. I will give you the links so you can view them. These ship manifests have a lot of information on them about where they were going, where they came from, plus information of about people they knew in the country they came from and they country they were visiting. I think it said on one that Antonio could not read so this could partially account for the spelling variations of the last name.