What are the sayings of scholars regarding the ruling on congregational takbir, and is its permissibility inferred from the actions of Ibn Umar and Abu Hurairah (may Allah be pleased with them both) in the marketplace, where people would say takbir because they said takbir?

Ibn Umar and Abu Hurairah's going out to the market to perform the takbir was to remind people of their heedlessness, not for an organized, communal takbir. Imam Shafi'i's statement about performing takbir individually and communally does not refer to the well-known contemporary form of starting and ending with one voice. When a statement is open to possibilities, it loses its evidential force. Communal takbir with one voice is an innovation (bid'ah), and prominent imams, including Ibn al-Hajj, have explicitly stated this.