2.) What does this mean for children with only a mother or only a father or neither?
I can tell you exactly what it meant for me. I had neither. I was born in 1987. According to my Grandmother I was the product of a one night stand between my father and biological mother, of whom I never knew. My father dumped me on my Grandmother four years later in 1991, and fled to Australia. I was 15 years of age before my father came back into my life in 2002, as a married man with a step daughter. I lived with him until 2007.
My father was not prepared to be a parent, and thusly our relationship with one another suffered because of it. He tried to insert his wife into the mother role, not understanding I saw my grandmother as my mother figure. It angered my Grandmother to no end, which spurred familial chaos, leading to frequent arguments between them. On top of that, he tried to assign parenting roles to my then step sister which infuriated my grandmother greatly. None of his actions went over well.
My father became became quite overbearing, forcing himself into the parenting role, when my Grandmother had raised me all of the time he was gone. What he didn't understand was that he couldn't simply supplant my grandmother as my primary parenting figure. Later on, he asked for my grandmother for child rearing advice but never took it, electing to elicit parenting advice from the internet, once again, leading to further resentment between he and I. All of that familial chaos eventually led to his wife walking out on him with another man. He left Athens not soon afterwards.
He made my life a living hell during high school, but yet I still managed to press on and graduate with honors. That's where my endeavors for a successful career essentially ended, no thanks to my father.
Finally, in the fall of 2006, I dropped out of college, in the spring of 2007 I lost my job. My father and I had made a standing agreement that if I maintained a job and attended college, he would offer me room and board for a nominal fee. Well for a time I did just that. But the aforementioned events took place. Upon my departure from the campus of Athens Technical College that day, I simply stated to my grandmother that the familial chaos my father was inciting was having a tremendous, negative effect on my studies. I couldn't go on. I was drained, and emotionally spent. On New Year's day 2007, I rung in the New Year by learning that I was being arbitrarily evicted. He never knew, nor was he aware that his chaotic influence had caused me to drop out of college.
I spent the last five months of employment fending for myself at my Grandmother's house, watching movies and playing Halo on the PC. She wasn't living there, though, but with my father at his home with a medical condition. I was completely cut off from my family, with occasional visits from my grandmother to bring me whatever she cooked for dinner for the rest of the family that night.
My father never assumed his proper role as a father figure, leaving my grandmother to be the only mother figure I ever knew. I never really lived in a stable family. I could have benefited from having an actual mother and a father, but my grandmother had to be the stand in. She did one hell of a job.
I'm here to testify for the emotional need for a mother and father to be there for the child. I was essentially abandoned my my parents, but by the grace of God he sent an angel to rescue me, my Grandmother, once again.
I can tell you how alienated I felt watching all of the children at day camp leave with their moms and dads, and how many times I asked my grandmother where my biological parents were. I will disagree adamantly against those who say that having a mother and a father isn't essential for a child. You are dead wrong.
(Sorry for the autobiography, but this is the best way I knew how to address your question.)