The question is: what can you not do while on your period? The answer is: prayer and fasting, only. For everything else, the sky is the limit! So you can still recite Qur’an and you can still make du’a to your heart’s content. You might not be able to pray Tahujjud or Tarawih, but you can still stay up and make plenty of du’a. You can also, of course, continue to perform acts of sadaqah; one of the coolest acts of sadaqa for the non-fasting person is preparing meals for those who are fasting, as the Prophet (SAW) said, “Whoever gives iftaar to one who is fasting will have a reward like the fasting person, without detracting from the reward of the fasting person in the slightest.” (Sunan at-Tirmidhi, graded Sahih)