Given that Hideyoshi had very few relatives, and he had his nephew and his entire family put to death, and Ieyasu did the same to Hideyori, I doubt there would be any relatives left. Apparently, there was one girl child by the name of Okiku who was spared from his nephew's family, but I don't know whether or not she went on to have any descendants.
I think so. He was very close to his brother, and was appointed guardian of Hideyoshi's first son. Hidetsugu (who was the son of Hideyoshi's sister) wasn't named heir until after Hidenaga's death, which would lead one to believe that Hidenaga would have been the preferred choice. In turn, that would imply that had Hidenaga had any offspring, they would have been chosen over Hidetsugu. I'm happy to be proven wrong over this though, as I don't know the answer for certain.
Also, I can't see Ieyasu leaving any threats like that alive to challenge him.
It is obvious. Hideyori and his mother stayed in Osaka castle and Iyeyasu hear that Hideyori is building an army.Iyeyasu waged a mini war and Hideyori's castle fell and the PBS documentary said that Iyeyasu killed every body who stayed along with Hideyori in the Osaka castle . Since Iyeyasu had respect for Hideyoshi, he asked Hideyori and his mother to commit seppuku. Later he grieved for asking Hideyori to commit seppuku and He wrote buddha's name ten thousand time for repenting his mistake.