Is it permissible for women neighbors of the mosque to follow the Imam of the mosque in all prayers, and specifically in Tarawih prayer, knowing that the Imam's voice is clearly audible due to loudspeakers?

It is not permissible for neighbors of the mosque to follow the Imam in the mosque, and merely hearing the voice does not validate the following. Similarly, it is not permissible for women to follow the Imam if their prayer area is separated from the mosque by a residential house.