Does the following relationships constitute a "family"?

I cant say what consitutes family for someone else. But I would consider all of these family.
Also, your survey is biased. The straight couple has only lived together for 3 months, but you dont say how long them have been together total, while the gay couple has been together for 5 years, but you dont state how long they lived together.
On number 3, you dont state the kind of contact he has. You can still be a dead beat dad and have contact. You also dont say what kind of contact.

In the end, each person makes their own judgements about who they consider family. I dont think it is anyones place to say the relationship isnt family accept the people directly involved.

yes
yes
yes
if she considers him "family"
yes
yes

family is whoever you feel close to, whoever you love, whoever you want in your life for the rest of yourlife regardless of blood or marriage ties...

who are we to judge other people's "familia ties"

I know my biological father and step mother, and normally those are the people you'd call your family; however for us, we were never close, more like strangers living in the same house. I have found family in others... my roommate from the group home is like my sister, my high school sweet heart has become a brother figure, my husband...they are my family, the people I wouldn't know how to live without

If you're happy with your spouse or the situation, then that's what family means.

Yes to all. Family is what you make of it. There are (or shouldn't be) any rules. If people love one another and call themselves a family then that is what they are.

1. A gay couple who have lived together in a stable relationship for 5 years in a home rented in the sole name of one of them? YES

2. A heterosexual coupla with no children who have lived together for 3 months in a home rented in the sole name of the woman? YES

3. An unmarried father who lives alone but has contact with his 3 year old son each weekend? The son lives with his mother YES

4. An elderly woman who has shared her home with a younger man for ten years who acts as her unpaid home help whom she treats as a nephew? YES

5. A married couple with no children who each own their own home and whose jobs mean they live apart for all but 4 weeks a year? YES

6. A 15 year old girl, orphaned at birth who has grown up in the home of a married couple with 3 children of their own, but was never formally adopted? YES

i think 2 is the only one that doesnt costitute as a "family"

the last one, based on the description

In psychology, a family is generally defined by the individual. A family is a home base where they know they can come home always and be accepted. What that means varies a lot from person to person.