There is no basis in the Sunnah for saying du’a between one salam and the other during Tarawih prayer by saying “Subhanaka Rabbana wa bi hamdika Allahumma ighfir lana.”

There is nothing wrong with repeating the same Surah in the Tarawih prayer, or in any other prayer. A person may recite a Surah in the first Rak`ah and repeat the same Surah in the second.

Praying tarawih prayer in congregation in the mosque is better, but if a man prays tarawih on his own at home, or in congregation with his family, that is permissible.