Is it permissible to refuse a suitor because he does not own an apartment?

Firstly: 

If the one who is proposing marriage is acceptable in terms of religious commitment and good character, and he is able to provide accommodation, even if that will be after some time, then he should not be refused, because the Prophet (peace and blessings of Allah be upon him) said: “If there comes to you one with whose character and religious commitment you are pleased, then marry (your female relative under your guardianship) to him, for if you do not do so, there will be tribulation and great mischief on earth.” Narrated by al-Tirmidhi (1084) from Abu Hurayrah; classed as hasan by al-Albaani in Saheeh al-Tirmidhi. 

But if he is not able to provide accommodation, or he needs a lot of time until he can afford it, then there is nothing wrong with refusing him, because of the harm that will be caused to the girl by tying her to him and waiting a long time to get married. When Mu’aawiyah ibn Abi Sufyaan proposed to Faatimah bint Qays (may Allah be pleased with them both), Mu’aawiyah was poor, and the Prophet (peace and blessings of Allah be upon him) advised her to refuse his offer, because he was poor and had no wealth. Narrated by Muslim (1480). 

This suitor who is unable to afford the expenses of marriage is addressed by the words of Allah (interpretation of the meaning): “And let those who find not the financial means for marriage keep themselves chaste, until Allah enriches them of His Bounty” [al-Noor 24:33] and  by the words of the Prophet (peace and blessings of Allah be upon him): “O young men, whoever among you can afford to get married, then let him do so, for it is more effective in lowering the gaze and guarding chastity. And whoever is not able to do that, then let him fast, for that will be a shield for him.” Narrated by al-Bukhaari (5065)and Muslim (1400). 

Secondly: 

It is not prescribed to recite al-Faatihah at the time of engagement, because that is not narrated from the Prophet (peace and blessings of Allah be upon him). 

Thirdly: 

The mahr and accommodation are the rights of the wife, and she may be content with a little of that. Her guardian should help her to be chaste. If she accepts someone whose religious commitment and character are pleasing, and he has enough to provide accommodation and the mahr, then it is not permissible to prevent the girl from marrying. But if he does not have anything, then the guardian may refuse the proposal, because the girl’s agreement in this case is based on emotion and lack of experience, and perhaps she is deceived by the suitor. 

Fourthly: 

It is not permissible for a girl to form a relationship with a non-mahram man, whether he has proposed marriage to her or not, because of the bad consequences to which that may lead, as is obvious, especially if her family have refused his proposal; in that case there is no justifiable reason for him to speak to her. 

See also questions no. 45668 and 36807 on the ruling on speaking and correspondence between a suitor and his fiancée. 

May Allah help us all to do that which He loves and which pleases Him.