There's good information here, but I do have a couple of questions. On the Ellis Island record, it states that Rosa Randazzo was meeting her husband, Joseph Guercio. That conflicts with the census record giving his name as Giovanni which translates to John. Also, from the 1930 census record, you state that they were married in 1930. I can't find anything on that census record about marriage. What column is that in? Before that, you had stated 'by this marriage record' that they were married February 23, 1930, but there's no copy of the marriage record.
You state that you found the immigration record of Joseph's mother - Rosa Guercio. However, the census record you produced for 1910 indicates that his mother's name is Carlina and that she is 25 years old in 1910. Rosa is 33 years old in 1901 which would make her 42 years old in 1910. They can't be the same person.
sorry in the search I saved some Guercios, 1910 census, and I posted one but the Rosa Randazzo is of the other Joseph Guercio( that I found and born abt in same year); so the 1910 census of Joseph Guercio son of Joseph Guercio and Rosa Randazzo is: 1910 United States Federal Census about Joseph Guercio Name: Joseph Guercio Age in 1910: 9/12  Estimated Birth Year: abt 1910  Birthplace: New York Relation to Head of House: Son Father's name: Joseph Guercio Father's Birth Place: Italy Mother's name: Rosie Guercio Mother's Birth Place: Italy Home in 1910: Manhattan Ward 12, New York, New York Marital Status: Single Race: White Gender: Male Neighbors: View others on page Household Members: Name Age Joseph Guercio 45 Rosie Guercio 39 Salvatore Guercio 13 Frank Guercio 11 Annie Guercio 7 Bessie Guercio 5 Thomas Guercio 3 Laurence Guercio 2 Joseph Guercio 9/12 
abt the column you can see in column 15.. however in the data that you provided are some discrepancies and I search but nobody sure results abt the people that you are searching for...
Okay, it appears a puzzle to be solved as to which 1910 census to believe. I feel comfortable about the 1930 census of just Joseph and his wife Mollie because that was her nickname and the age confirms the time she was born plus it confirms that she was born in New york. that's 3 facts that match what I know about her. Therefore, since the 1930 census says her husband was 22 years old, implying he was born in 1908 or 7, then the new census you just gave me where he is less than a year old in 1910 implies that this Joseph would have only been 21 in 1930 instead of 22 as the 1930 census that appears accurate for his wife, states. Therefore, I don't think that my Joseph Guercio is the one in the latest 1910 census you gave me. If only we could find a marriage certificate, then we would have his parents and be able to conclusively identify his family.
Since that post, your cousin, Robert Guercio, has been in contact with me. I have that 1940 census. Robert told me that your dad Eugene (his uncle)had family information and might contact me, but I haven't heard from him. I have no information on your dad's wife nor children. You and I would be second cousins. I am interested in learning more about your family. Please contact me directly at firstname.lastname@example.org.