1) How should a menstruating woman spend Ramadan days and nights of Qadr?

2) Is it OK to pray Tahiyyatul mosque prayer in a place which is rented for Ramadan to perform Taraweeh prayer?

1) She can do zikr, make dua, read and study Islamic knowledge.

2) Tahiyyatul masjid is specific for the masjid and does not apply to the musalla.