Is it permissible for a woman in Ramadan to increase the number of verses in a single rak'ah to compensate for the surahs she missed reciting during her menstrual period, or is it better for her to continue praying without compensating for what she missed?

If the questioner's sister is following the Imam in Tarawih prayer from her home, then it is permissible to follow from behind a barrier out of necessity, provided she hears the Imam's voice. She should not recite anything behind the Imam except Al-Fatiha and listen attentively to his recitation. However, if she is praying alone, her prayer is not connected to the Imam's prayer, and she may recite whatever surahs she wishes. Increasing the recitation of the Quran is recommended, especially in Ramadan, and completing the recitation of the Quran in Tarawih is also recommended.