Is it permissible for a Muslim woman to marry a man who feigned Islam to appease his wife and her family, then buried her after her death in a non-Muslim cemetery and in a non-Islamic manner despite the availability of a Muslim cemetery, and is it permissible to recite the Quran and supplicate for her at her grave in this cemetery?

The basic rule is to prohibit burying a Muslim in a non-Muslim cemetery unless there is a necessity. If a Muslim is buried there and it is possible to transfer the body to a Muslim cemetery without fear of decomposition, then it is obligatory to do so. Otherwise, there is no blame. Reciting the Quran at the grave is disliked, but there is no impediment to reciting it elsewhere and dedicating its reward to the deceased. It is permissible for a woman to visit that cemetery for admonition and to supplicate for the deceased.