My first question would be, how old is this child? But I guess it doesn't matter because I believe that anyone below the age of 15 should have their mother present.
(1) Do you feel that it hurts a child to have the mother gone for many hours each day? Why or why not?
Yes, but my perspective is very biased because my mother was very overprotective and therefore made a huge influence in my upbringing. Generally, without her, I wouldn't be the man I am today. She thought many important lessons and was the "go to" parent for most problems. Nonetheless, I think that this question depends on if the other parent is present. If at least one parent is present then it's okay, so I wouldn't know the differences between not having a mother or father figure. But yeah, I have a closer relationship with my mother as she was a stay at home mom until I was like 14 years old.
(2) Who should care for a child while the mother is working? Why?
The other parent. If that is not possible then it should be a much older sibling or other family such as an aunt or an uncle, why I feel this way is because the influence these figures would have, should theoretically resemble what the mother would have. Strictly speaking about upbringing here, and not so much focus on emotional effects. But an older sister would be ideal from this perspective I guess.
(3) Assuming a mother does not have to work, do you feel that putting a child in day care is more beneficial than staying at home with the mother?
There should totally be a mix between the two. As I said my mother was at home for the most part, but I still went to day care as a kid and I still remember my friends, my teachers and things I did there. Being too attached to ones mother for a long period as a child could really have some negative effects as you grow older. My mother was not afraid to let me go to day care, but she would always wave in the morning when I left, and welcome me back home in the afternoon. Therefore, I think that a child should definitely get the best of both worlds, nothing but positive in mixing the two.