Q 2: The Messenger of Allah (peace be upon him) enjoined the believing man who is seeking marriage to look for a religious wife. (Part No. 18; Page No. 189) The foregoing is well-established through the renowned Hadith which reads,
A woman may be married for four reasons...
the ruling if I love a girl who is not fully religiously committed because she does not wear Hijab (veil)
but when I discussed this issue with her she mentioned that she is ready to make Tawbah (repentance) to Allah and obey Him (Glorified and Exalted be He). Shall I marry her and get two rewards; the reward of marrying and protecting my private parts (from illegal sexual acts, etc) and the reward of helping to guide the concerned girl (to the way of Allah) or should I not proceed to marry her and look for another religious wife?
If the reality is exactly as what is mentioned in the question i.e. the concerned girl is ready to wear Hijab and make Tawbah to Allah (Glorified be He), it is permissible for you to marry her if she is a chaste Muslim or one of the people of the Book. May Allah guide her and enable you to protect your private parts and help you direct the concerned girl to the way of Allah. May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.