Is it true that the prostration of recitation (sujud al-tilawah) does not require a takbir when prostrating or rising from it, and if the imam says the takbir, he should not say it aloud, and how do the congregants know about the imam's prostration and rising from it in an audible prayer?

The prostrator of recitation (Sajdat al-Tilawah) should say the Takbir aloud when lowering and raising, based on the hadith (definition) of Ibn Umar that the Prophet, peace and blessings be upon him, used to say the Takbir aloud when prostrating. This is also supported by the general hadith of Abu Hurairah and Ibn Mas'ud, which states that the Prophet, peace and blessings be upon him, and the Rightly Guided Caliphs used to say the Takbir at every lowering and raising.