Must the man marry the girl he lied to and promised to marry, then caused her to become pregnant and have an abortion? Is aborting the fetus in its second month considered a crime of murder? And how can he repent from this sin?

You are not obligated to marry the woman with whom you committed adultery. In fact, according to the more authoritative opinion, it is not permissible to do so unless she repents to Allah Almighty. If she aborted the fetus, you are not responsible for its blood money; rather, it is incumbent upon the one who directly carried out the abortion. However, you must engage in sincere repentance and multiply your good deeds because you assisted the girl in committing sin.