How does one pray behind the Imam, from the Takbir to the Taslim, and are there any proofs that the Imam says the Takbir aloud while the worshiper says it silently?

The description of the congregant's prayer is the same as the description of the Imam's prayer, and the most important differences are that the Imam vocalizes the takbir, while the congregant whispers it and does not vocalize it. This is what the hadiths, the consensus of scholars, and the practice of Muslims have indicated. It is disliked for the congregant to vocalize the takbir because it may disturb the worshipers, and because the Imam vocalizes it to be followed, whereas the congregant has no need to vocalize it. The Malikis made an exception for the takbirat al-ihram (definition), permitting the congregant to vocalize it.