Although the main question is answered by @Daniel, I want to highlight and elaborate the second para of OP's question.
Amado used the DNA from Jiraiya’s severed arm, which had been ripped off by Pain before the rest of the body was thrown into the sea to clone him. It was never explained what was done with Jiraiya’s arm, and Kabuto could not find it during the war. But perhaps Amado had come to the place first and collected the arm before anyone else came looking for it.
Yes, it is true that Jiraiya wasn't revived in the final arc of NS by Kabuto through Edo Tensei and the reason for that is quite different in anime and manga. In Masashi Kishimoto's original story in manga, Kabuto claims that he could get a big enough sample of Jiraiya's DNA to reanimate him, but Obito says not to push his luck. However, in the anime, Kabuto simply says that he can't reanimate Jiraiya because his body is at the bottom of the sea. Considering all the other powerful ninja Kabuto brings back, this is a weak excuse, especially since he can go through great lengths to bring back DNA of dead ninjas. The real reason Jiraiya isn't reanimated is to protect the integrity of the character's emotional final scenes in NS. But if we consider the context of the narrative, his omission in the final war is certainly odd.
Now, the absence is somewhat explained in Boruto. Kashin Koji is thought to be a clone of Jiraiya because Kara were heavily involved in genetic manipulation and the concept of clones is already known in Boruto i.e. Shin. So, Kara might have took the severed arm of Jiraiya for themselves leaving Kabuto with nothing to work with. Kara have been operating in secret for years, and they were artificially creating ninjas appears to be their chief recruitment method. Even if Kabuto did manage to get some DNA, he cannot ressurect him because Kashin Koji was already a clone of him and the rule of Edo Tensei is that the body must be dead in the first place in order to get reanimated.