Is it permissible to join the Tarawih prayer with the intention of praying 'Isha, and is it better to establish a separate congregation for 'Isha prayer?

It is permissible to be led in prayer by someone praying Tarawih if one is praying Isha. It is also permissible to pray Isha in a separate congregation and then join the Imam for Tarawih. If the Imam is praying Tarawih, it is permissible for someone entering the mosque to pray the current Isha prayer or make up missed prayers. As for the Witr prayer in this situation, there are two opinions, and the apparent one is that it is not permissible. It is forbidden to begin Tarawih if the Imam is already praying it.