Is it permissible to perform Tarawih prayers at home in congregation instead of at the mosque, and is it permissible to pray them silently rather than audibly?

Performing Tarawih prayer at home is permissible, but it is better to pray it in congregation at the mosque, due to the Prophet's (peace be upon him) saying: "Whoever prays with the Imam until he finishes, Allah will record for him the prayer of a whole night." The original practice in it is to recite aloud, but reciting aloud and silently is a sunnah (recommended practice) of the prayer, not an obligation. So, if the Imam recites silently in a prayer that is meant to be recited aloud, his prayer is valid but incomplete. As for an individual praying alone, they have the choice between reciting aloud and silently.