Add a person to tree who has no direct relationship

Did you have any luck with the 1900 census? (Unfortunately the 1890 census got accidentally burned up, to the frustration of genealogists everywhere.)

Does maternal grandfather have the same surname as head of household, or does it match wife of head of household, or neither? That should give some clues as to which side of the family he fits on. "Cousin" is a somewhat indefinite term, but it may be simplest to assume maternal gf and head of household were first cousins (until/unless you learn otherwise).

If the names match, easy-peasy: their parents were (probably) brothers; make an "NN" profile for maternal GF's father, add "Brother of NN", then add the rest. (Same deal if the match is to "Wife of head of household", which would actually make him a "cousin-in-law".)

If there isn't a match, assume maternal gf was a *sister's* son pending further information.

The tree can always be corrected as more information comes in.

Thanks for the ideas (I'm brand new at this). Nothing in 1900 Census. I'm pretty sure he arrived through Ellis Island in 1903 but an Ellis Island search comes up empty. He's in the 1020, 1930 and 1940 Census. I believe he died in 1941 but I haven't checked the records yet. His name in the 1910 Census is Herman Swiridow and in subsequent Census's he's Herman Sviridow which is the last name his family went by.
The 1910 Census Head of Household is Abraham J. Arensberg, his wife is Sophie M Arensberg. The Brother-in-law is Michael M Schwer. My Grandfather is Herman L Swiridow - Cousin.
I just started to do the searches on the other names but haven't come up with any matches yet.
I agree with your assessments of the probable relationships.
I also just started to do DNA. Tested autosomal DNA at My Heritage (which I understand is Family Tree) and have transferred results to GEDMATCH. I have some matches on both but don't want to contact anyone yet. I need to learn more. From some of the reading I've done I'm going to test autosomal at Ancestor and 23.
One of the reasons I'm prioritizing this is the Ethnicity. Since all 4 of my grandparents are from Russia / Latvia, I expected the test to come back almost 100% Ashkenazi Jewish. Instead it came back with 80% Ashkanazi Jewish and 18.5% Italian, 2 non-geographically overlapping regions. Obviously, my curiosity is very aroused. My Trees on My Heritage and Geni are almost duplicates and completely on my grandmother's side. None of the 700+ dna matches have any more than trace Italian. This leads me to the path of one of my grandfathers. I'm thinking that a detailed Y Test might provide some information. I don't have a lot of places to go to get others to do DNA tests on the maternal side that might help. My maternal grandparents had 4 girls. Two had no children. The other two (twin sisters) married brothers. I have 2 what I refer to as double 1st cousins. They're going to get tested but I don't see where their test will be much different than mine. My father also had a sister and some of my1st cousins would probably be willing to do a DNA test.
One of my mothers sisters had some hand written notes and I'm trying to locate them now.
Sorry to have bored you but I'm hoping that you'll tell me if I'm off in a wrong direction and/or offer some additional thoughts about how to proceed. It almost seems like an adoption search.

George, is this your grandfather:

Herman Louis Sviridow
born 1 Jan 1879 or 1 Jan 1881 in Nevil, Russia
died 21 Jun 1942 in Bronx, NY
buried in Mount Carmel Cemetery Glendale Queens
arrived in NY 4 Nov 1903
naturalized 20 Sep 1906 in NY
married Mabel Josman 22 Sep 1910 in Manhattan

Oton, yes it is. I can see that I have a lot of learning to do. My searches on immigration, naturalization, death, burial and marriage date and location came up empty.

Thank you so much.

Oton, Thank you for the updates you did to so many of the profiles in my tree.

All this information is most easily found on ancestry.com. (but you need a paid account)
There is also marriage between Lillian Sviridow to Teophile Alexander on 22 Oct 1949 in Manhattan. I couldn't find any other record to corroborate this but you can enter it if you think it is correct.

I'm going to start an Ancestry acccount (they have a sale on right now).

I was at my Aunt Lillian's wedding at the Gramercy Park Hotel. My parents introduced them and they lived in the same apartment building as we did after the marriage.

Bertha (my mother) and Dinah, twin sisters, married brothers Julius and Samuel Kulman at a double wedding on the girl's 20th birthday. The first child in each family was born 7 years later. My cousin Richard was born 16 hours before me (different days) and the mothers shared a hospital room

Another issue, about Fred Kaufman. His obituary http://www.nytimes.com/1977/10/20/archives/deaths.html states his wife was Sarah Sviridow and he had 3 children Edward, Jerry and Annette. But elsewhere I found census records where these children's mother was named Adele. Did Fred have 2 wives?

Yes, Sarah was his second wife. It was a marriage later in life and they had no children together. I don't know the details of the end of his first marriage or how Fred and Sarah met. I never heard any discussions about his prior life. I didn't see them that often and I don't have any strong memories of his children. As an aside, he was a very nice person.

Sarah's first husband was named Jack. I don't know his last name. When my father was in the US Navy in WWII, Sarah lived with my mother and me since Jack was in the Army. I don't know what the end of their marriage was but I have no memory of ever meeting him.

As an aside, it's interesting thinking back to events over 70 years ago and being able to pull up details. Sarah got me into doing the NY Times Sunday Crossword with a pen. Also eating breakfast and having my morning coffee while standing at the kitchen counter and reading the newspaper.

Changing back to my Grandfather, Joseph Kulman. I joined Ancestry and uploaded a GED. Then I did a search and found that he was in other Trees. Research showed me that most of them had errors which had bee created as as result of the 1910 Canadian Census. The family lived in Ste. Agathe des Monts, Quebec and the census taker was obviously a French-Canadian speaker. There were few English speaking families and just a couple of Jewish families. The census taker, probably through language difficulties on both sides listed Juliette instead of Julius and added a second 1906 birth with an unknown father.

In any case, one of he trees belongs to my deceased sister's niece through marriage and we talk and text regularly, so I texted her and asked if she wanted me send her all of the corrections or did she want me to update the records for her. That was easy.

The others aren't as easy since I don't know the tree manager/owner. My question is: How does one approach the person without offending them, especially since they have him in their tree and I'd like to explore the relationships with them.