Is it permissible to pray Tarawih and Tahajjud in the mosque while having memorized only 5 surahs and not being proficient in the Arabic language, or is it better to pray at home and use a copy of the Quran written with English letters? And what is the difference between Tahajjud prayer and Tarawih prayer?

A woman's prayer in her home is superior, but her prayer in the mosque might be better if there is a benefit, such as benefiting from lessons or being more active in prayer, or fearing laziness at home, provided she observes modesty and proper covering. Tahajjud is the night prayer performed after sleep, while Tarawih is the night vigil (Qiyam al-Layl) during Ramadan.