Is this relationship brotherhood for the sake of Allaah or a relationship that is not acceptable according to sharee’ah?
Question

                I am a religiously committed (praise be to Allaah) young man, studying in University in a Muslim Arab country, in which many young people have gone astray from Islam. It has become difficult to find righteous friends as the Messenger (peace and blessings of Allaah be upon him) advised us to do and as is enjoined in the Holy Qur’aan. A while ago I got to know a girl who wears hijab, and she is the reason why I was guided. We only met on the bus or in the university in order to talk about religion and our love of Allaah, and to encourage one another to memorize Qur’aan and pray qiyaam al-layl, and to forbid one another to do things that Allaah has forbidden of indulging in falsehood and other mistakes that a person may make without realizing it. I started to long to meet her, because I found that speaking to her strengthened my faith and she helped me to keep on the straight and narrow. But I am confused about how to categorize this relationship and I am not sure whether to continue it or stop it, because she is not one of my relatives.

 Can I regard her as my sister in Islam?  Is it permissible for me to speak to her on the bus or in the university? Is it permissible for me to look at her face?.
Praise be to Allah.
      Many people make the mistake of thinking that the 
      difficulties of our times and the lack of brothers and the corrupt 
      circumstances make it permissible to do things that may lead to their 
      doom, and they fall into the traps of the Shaytaan. 

    Yes, beware of being deceived by the Shaytaan, who makes sin 
    appear to you as obedience, and comes to you through a door which you think 
    you have shut on him, for the Shaytaan keeps knocking at the doors of 
    misguidance and trying to open them to the slaves of Allaah and make them 
    fall into his traps. 

    Have you not heard the words of Allaah (interpretation of the 
    meaning): 

    “(Iblees) said: ‘Because You have sent me astray, surely, 
    I will sit in wait against them (human beings) on Your straight path.

    17. ‘Then I will come to them from before them and behind 
    them, from their right and from their left, and You will not find most of 
    them as thankful ones (i.e. they will not be dutiful to You).’”

    [al-A’raaf 7:16, 17]? 

    Ibn al-Jawzi (may Allaah have mercy on him) said in 
    Talbees Iblees (p. 52): 
Iblees tricks people in 
    whatever way he can, and his power over them increases and decreases 
    according to their alertness or negligence, their ignorance or knowledge. 

    Note that the heart is like a fortress, and the devils are 
    always going around the fortress watching for the guards to become heedless. 
    The guard should know all the gates of the fortress which he has been 
    appointed to guard, and he should not let his attention slip for a moment, 
    for the enemy never lets his attention slip. 

    A man said to al-Hasan al-Basri: Does Iblees sleep? 

    He said: If he slept, we would have a break! End quote. 

    The situation which you are asking about is one of the traps 
    of the Shaytaan. How many fires have been lit in the hearts of young men, 
    the first spark of which was a look or a smile or a meeting or a 
    conversation, and how often does that happen under the guise of 
    companionship, mutual advice and calling people to Allaah. 

    When Islam forbade free mixing between men and women, and 
    forbade a man to be alone with a non-mahram woman, or to look at her or 
    shake hands with her, it was paying attention to the evil consequences of 
    such matters. Allaah is the Creator of mankind, and He knows best what is 
    good for them and what is bad for them. 

    The Prophet  (peace and blessings of Allaah be upon him) 
    said: “No man is alone with a (non-mahram) woman, but the Shaytaan is the 
    third one present.” Narrated by al-Tirmidhi, 2165; classed as saheeh by 
    al-Albaani, 1758. 

    What this means is that the Shaytaan is present with them and 
    provokes desire in each of them until he causes them to commit zina. End 
    quote from Tuhfat al-Ahwadhi. 
It was narrated from 
    ‘Ali ibn Abi Taalib that a young woman from Khath’am came to the Prophet 
     (peace and blessings of Allaah be upon him) and asked him a question. 
    Al-Fadl ibn ‘Abbaas was riding behind him on the camel and he turned his 
    face away. Al-‘Abbaas said: “O Messenger of Allaah, why did you turn away 
    your cousin’s face?” He said: I saw a young man and a young woman and I did 
    not feel sure that the Shaytaan would not try to influence them.” 

    Narrated by al-Tirmidhi (885); classed as saheeh by 
    al-Albaani in Saheeh al-Tirmidhi. The hadeeth is also narrated in 
    al-Saheehayn. 

    It says in Fataawa al-Lajnah al-Daa’imah (12/163): 
Free mixing of men and 
    women for education is haraam and is a great evil, because it involves 
    fitnah, the spread of immorality and transgression of the sacred limits. The 
    evil and moral corruption that has happened because of this mixing is the 
    strongest evidence for it being haraam. End quote. 

    The Committee was also asked (17/66) the following question: 

    What is the Islamic ruling on friendships with the other sex, 
    knowing that this friendship is decent and chaste and is known to all, with 
    nothing hidden? 

    They replied: 

    This is one of the most serious of haraam actions and the 
    worst of evil deeds. It is not permissible for a woman to make friends with 
    men who are not her mahrams, or vice versa, because that is a means that 
    leads to fitnah and falling into evil deeds. End quote. 

    With regard to looking at her face, we have stated in the 
    answer to question no. 1774 that deliberately looking at a non-mahram woman 
    is haraam. 

    Our advice to you is to make a decision about this 
    relationship. Either take her as your wife, if this girl is 
    religiously-committed and of good character and you have grown fond of her, 
    or cut off this relationship with her and close this door, for it is the 
    door to evil and immorality, so do not leave it open lest you then regret it 
    when regret will be to no avail. 

    See also questions no. 1200
    and 22702. 

    And Allaah knows best.