Is it permissible to reject a suitor because of the unavailability of an apartment, and to refuse to recite the Fatiha for the same reason, knowing that the girl approves of him? And is it permissible for the girl to converse with the young man without her family's knowledge?

If a suitor is pleasing in his religion and character, and is capable of providing housing even if after some time, then he should not be rejected, based on the saying of the Prophet (peace be upon him): "If someone whose religion and character you approve proposes to you, then marry him off. If you do not do so, there will be tribulation on earth and widespread corruption." However, if he is unable to provide housing or needs a long time, there is no harm in rejecting him. The Prophet (peace be upon him) advised Fatimah bint Qais to reject Mu'awiyah due to his poverty.

Reciting Al-Fatiha during engagement is not prescribed because there is no evidence for it.

The dowry and housing are rights of the woman, and she may accept little. The guardian should assist her. If she accepts someone whose religion and character are pleasing and who possesses what is suitable in terms of housing and dowry, then she should not be prevented. However, if he possesses nothing, the guardian may refuse.

It is not permissible for a girl to establish a relationship with a non-mahram (definition) man, whether he is an engaged suitor or not, due to the ensuing harms.