Not at all. Yuji Itadori's story doesn't end with his execution in the manga. There are many developments and challenges he faces, but execution isn't one of them.
Yuji Itadori survives till the end. The manga doesn't have his death as the final outcome. The story might have thrown challenges at him, but he manages to overcome them and remain alive.
It's hard to give an exact time as it depends on the manga's plot development. But typically, Yuta Okkotsu shows up when certain events and character arcs lead to his introduction.
The Qing Emperor's attitude toward Fan Xian was not clear. The first document mentioned that the Qing Emperor was hostile to Fan Xian and hoped to eliminate him to prevent him from becoming a disaster in the future. However, the second document described the Qing Emperor's despicable methods of revenge and humiliation against Chen Pingping, and his execution. The third document mentioned that the Qing Emperor had killed Ye Qingmei but not Fan Xian. Thus, from the information provided, the Qing Emperor wasn't sure if Fan Xian wanted to kill him.
The Qing Emperor's attitude toward Fan Xian was complicated. He had helped him, schemed against him, and even thought of killing him. The Qing Emperor's feelings for Fan Xian had gone through four stages: probing, using, seizing power, and breaking up. In the probing phase, the Qing Emperor planned the Taiping Courtyard murder case and included Fan Xian's death. However, during the actual operation, some things that exceeded the Qing Emperor's expectations happened, causing Fan Xian not to be killed. Thus, the Qing Emperor was not clear about whether he wanted to kill Fan Xian. Therefore, there was no clear answer to the question of whether the Qing Emperor wanted to kill Fan Xian.