Why would anyone talk about their problemas at home with their bosses? Is this a US culture thing where work and non-work is blended so much that you mix and match conversations?

Both as a worker and a manager, I hardly know about other co-workers lives. Gay or not gay, married with kids, or eternal bachelor, I don't really have (or want) a clue about their private life, much less have a report tell me about his. Just say 'I am dealing with something, need some time off' and there, you got it, but I don't need to know your mother has cancer or you are going through a divorce. You are an adult, take the time and use it as you need.