Praise be to Allah.
What happened to you is one of the effects of staying in a kaafir country and studying in a mixed environment. Hence the scholars warned against that a great deal. We praise Allaah for having guided you and protected you from doing anything more serious than that.
You made a great mistake by deliberately breaking the fast during the day in Ramadaan. You should have asked Allaah to forgive you for what you did with that girl, and you should have completed your fast.
You should note that some of the greatest means that the Shaytaan uses to keep people away from the right path is to keep them from having good friends or from doing good deeds by making them think that they do not deserve that.
The result of this keeping away from good deeds and good people may be worse than the sin that led to it in the first place. Hence the wise man is the one who does not let one sin lead him to another, rather he hastens to repent from it and looks for more good people to be close to and does more righteous deeds. “Good deeds erase bad deeds.”
With regard to the emission of madhiy (prostatic fluid), this does not invalidate the fast according to the more correct of the two scholarly opinions. This is the view of Abu Haneefah and al-Shaafa’i, and was the view favoured by Shaykh al-Islam Ibn Taymiyah (may Allaah have mercy on him). Al-Mughni, 3/20; al-Ikhtiyaaraat al-Fiqhiyyah, p. 97. See also questions no. 38074.
But you are not certain whether you emitted madhiy or not.
No ghusl is required in the case of madhiy, but it is naajis (impure) and invalidates wudoo’, and it sufficient to sprinkle water on any affected areas of clothing. See question no. 34172.
You have to make up the day when you broke your fast, and repent to Allaah, but you do not have to offer the burdensome expiation, because that applies only in the case of intercourse, according to the more correct of the two scholarly opinions, which is also the view of al-Shaafa’i and Ahmad.
But if you have delayed making up that day until the next Ramadaan comes, then as well as making up the day you have to offer expiation for delaying it, by feeding one poor person half a saa’ of food, which is approximately one and a half kilograms. See question no. 38867.
And Allaah knows best.