Various masaail of Jamaat Salaah and Imaamat

Going into ruku' thinking that the Imaam made takbeer

Q: While praying Salaah in Jamat (congregation) a person was standing far from the Imam and also there were no speakers. At one point the person thought that Imam Saheb said Allahu Akbar, and so he was going to ruku. As he was doing so he found that the rest of the muqtatis were still standing (the person in concern heard it wrong) so he again stood up. Now my question is that is the Salaah of the person, in concern, valid or should he repeat his Salaah?

Hanafi Imaam reciting an Aayat of Sajdah according to Imaam Shafi'ee

Q: If a hanafi Imaam recites an Aayat of sajdah (that is according to Imam shaafi'ee Rahimahullah and not according to Imam Abu Hanifah Rahimahullah e.g: The Aayat of sajdah that appears at the end of the 17th juz) in salaah, and he is followed by muqtadis of the different mazhaahib, then what should he do in this situation. If he doesn't make sajdah will their salaah be valid? Is there a solution to this?

Should the Muqtadi complete his attahiyyaat and then stand up or should he follow the Imaam

Q: To recite attahiyaat is waajib in the 1st sitting of 4 rakaats Salaah. If it is missed then sajdah sahw becomes waajib. Sometimes the Imaam recites the attahiyyaat very quickly and then stands up whilst many muqtadees have not finished their attahiyyaat. Should they follow the Imaam immediately or should they complete their attahiyyaat and then stand?