I'm having the hardest time researching my great-great-grandfather, Frederick Hummel. What I know for a fact (coming to me as word-of-mouth from family members) is that Fred Hummel is the father of Minna Hummel and the husband of Minnie Walter. Documents that match this information are listed below:

1930 Census: https://familysearch.org/pal:/MM9.1.1/X4GZ-849 (Living in Mount Vernon)
1925 NY Census: https://familysearch.org/pal:/MM9.1.1/KSCQ-4GQ (Living in New Rochelle)
1920 Census: https://familysearch.org/pal:/MM9.1.1/MV3C-DYW (Living in New Rochelle)
WWI Draft Card: https://familysearch.org/pal:/MM9.1.1/KXYM-WGN (Living in New Rochelle)
1915 NY Census: https://familysearch.org/pal:/MM9.1.1/K95C-MJW (Living in New Rochele)
1910 Census: https://familysearch.org/pal:/MM9.1.1/M54W-JFQ (Living in New Rochelle)

Those are all of the sources that I have that I know are correct. Now comes the actual research. All of those state that he was born in New York around 1877 (the draft card states that it was February 1877) and that he worked for many years as a "sawer" or "mill hand" at a lumberyard. I've been searching and searching to find him in the 1900 and 1880 censuses to know the names of his parents, but I'm just not sure which of them is correct.

I have found that he married Minna Walter in 1905 in Kings County, New York, and I have found census documents showing him living with his parents Fred and Bertha Hummel in Brooklyn, which doesn't seem out of the ordinary based on where he got married. Those are not his parents, however, because that particular Fred Hummel was still living with his parents in 1910 while mine is documented as living with his wife in a different part of New York.

The only document prior to 1910 that I believe might be correct is this one:
1905 NY Census: https://familysearch.org/pal:/MM9.1.1/MV1W-CDC

It shows him living in Eastchester (not too far from New Rochelle) and more importantly, as a mill hand. This gives me his mother, Caroline, but I'm not sure if this is a reasonable approach or a large leap. Can anyone help me with this research?