What is the ruling on establishing multiple congregational Tarawih prayers in one mosque at the same time without using loudspeakers, and what is the solution to enable all huffaz to lead the prayer?

There is no impediment to repeating the Tarawih prayer in the same mosque, so long as there is a benefit in it and it does not cause disturbance. The Companions used to pray Tarawih in separate groups before Umar ibn al-Khattab, may Allah be pleased with him, gathered them behind a single reciter.