You pretty much answered your own question. Joseph wasn't emphasized as much because he had little part to play in the birth of Jesus, while Mary was a virgin mother, which was a really big deal.
What is hear is that he likely died, but the Bible doesn't specifically state why he wasn't present in Jesus' later life. I would think he'd at least visit Jesus' grave, but Mary came alone. Perhaps Joseph was too busy with his work at home, but I think the explanation that he was dead probably fits best.
I don't know if Mary had remarried. According to custom, a brother of Joseph's could have married her, and any children that would come out of that would be considered Joseph's. Also, I don't think widows were considered unclean. They might have been less desirable than the young virgin girls, but I don't know if there were any barriers to prevent a widow to be married again.
I don't know, and I don't know if we have any way of finding out. From what I've heard, it was likely that Mary was in her teens, but Joseph could have been as old as 40 or more. I would think Joseph would be a little more quick to find a wife than that, but I can't say anything for certain.
Yes. Mary knew that she was pregnant, and also that she had never slept with any men. But Joseph was uncertain, wanting to divorce her quietly at first. It took an angel to convince Joseph to keep her.
