I have some more info and questions:
The other Pietro Sclafani who died in 1907 was indeed the son of Francesco and Francesca. His wife was Vita Di Matteo and they married in Sciacca in 1870.
I have found the birth record for another child of Pietro & Liboria: Antonino Sclafani born 20 Nov 1886. This matches the age of Antonio on the 1905 census, but is considerably off from the age of Tony on the 1910 census. It's also way off from the age of Antonino on the passenger manifest, but I noticed something odd on that manifest: Above his name there's a word I can't make out and a number 18. If his age was 18 instead of 9, as it says next to his name, then his year of birth would be 1886. Can anyone look at this manifest and figure out what the word above Antonino Sclafani's name was?
http://interactive.ancestry.com/7488/NY ... turnRecord
I also found a tree on Ancestry (Stull, Redmond, Zimmerman, Seward, Crummitt) that has your Thomas Sclafani, b. 8 May 1888, and married to Anna Widers. He is also called "Gaetano" in the tree. The date of birth comes from a WWI draft registration card that has him as being born in NY. There is also a passenger manifest for Gaetano Sclafani from Sciacca in 1899, traveling by himself, to stay with a "brother" with a totally different surname. In a 1925 census (having him as born in Italy) he had wife Anna and children Peter, Bella, Frances, Gus, and Rhoda, which is definitely your family. Even though that tree has all these records attached to his profile, I'm not sure that they're all for the same person.
How do you know that Thomas Sclafani was born on 8 May 1888 in Sciacca?
Finally, I've checked 1886 to 1888 birth records in Sciacca so far and there no other Sclafani children born to a Pietro except the 1 that I found so far (Antonino). There is no Tommaso or Gaetano Sclafani, either. There was, however, a Gaetana Sclafani born on 10 May 1887 to Antonino Sclafani and Rosa Rizzuto, but it's probably just a strange coincidence.