Which is better in Ramadan: reading the Qur'an and completing it many times, or memorizing and reciting it, given the inability to combine both? And is performing Tahajjud with one's family better than performing Tahajjud in the mosque?

Reciting the Quran is a great act of worship, for every letter yields ten good deeds, and its merit increases in Ramadan. Memorizing and reviewing the Quran is better than merely reciting it, for the one who memorizes it will be treated specially on the Day of Judgment and will have a great status. As for the Tahajjud prayer, it is better to perform it in the mosque, unless performing it at home motivates and includes one's family.