All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger.
Hastening to repent from the sin of Zina (fornication/adultery) is obligatory, and Allah, the Exalted, is vast in forgiveness; He forgives sins no matter how grave they are.
There are conditions for a valid repentance that must be fulfilled and without which the repentance is not valid. To learn about these conditions, please refer to fatwa 86527.
Regret is an essential pillar in repentance; if you do not feel regret for committing the sin, then this means that the conditions for the validity of repentance are incomplete.
What you mentioned, that you do not feel regret in your heart, should not prevent you from repenting, as the devil may lure you because of this feeling and lead you to continue committing Zina. Rather, seek refuge in Allah, and hasten to sincerely repent.
On the other hand, perhaps you truly regret your sin but due to extreme fear one may imagine that he is not regretful, or the devil may lure him into feeling this way in order to tempt him, so beware of that.
You must completely cut any relationship with that girl if you want to be safe, so do not communicate with her by phone or through any other means.
If she sincerely repents and becomes righteous, then there is nothing wrong in marrying her. It is also acceptable to conduct the marriage contract and delay the consummation of the marriage and the Waleemah (marriage banquet). But it is better to not delay the consummation of the marriage too much. It should be noted that as soon as the marriage contract is conducted with a woman, she becomes lawful to her husband and they are permitted to have intercourse, but the customs and traditions of people in this regard should be taken into account. For more benefit, please refer to fatwa 88658.
You are not obliged to spend on your wife as soon as you conduct the marriage contract with her. Spending on her becomes obligatory once she allows you to have sexual intercourse with her or when she invite him to this.
With regard to your question: “Will it be Islamically acceptable if I ask her parents to financially support her?”; perhaps you mean that you ask them when you become obliged to spend on her and you are not able to do so. If this is the case, we say: you should not ask them because they might turn you down and this might cause some embarrassment to you, or perhaps this would give them a bad impression of you and you lose their respect. Also, asking people without a need is Islamically dispraised. But if her father takes into consideration that you are a student and helps you with the marriage expenses or with spending on your wife, then this is acceptable.
If marriage is not facilitated for you, then you should be patient.
If Allah predestines that she marries someone else, then there are many women other than her. What is important is that you cut your relationship with her because she is a non-Mahram to you, as we have already mentioned, and in order to be safe in your religion and your honor.
In conclusion, we warn against what happens in some Muslim communities regarding taking the free mixing of non-Mahram men and women lightly. Men are obliged to be firm and control the situation in their households, as their family is a trust with them.
Allah says (what means): {O you who have believed, protect yourselves and your families from a Fire whose fuel is people and stones, over which are [appointed] angels, harsh and severe; they do not disobey Allah in what He commands them but do what they are commanded.} [Quran 66:6]
Allah knows best.