What is the ruling on marrying a girl, if it is discovered after the marriage contract that she had a previous relationship with a young man who was not committed to religious principles? Is it obligatory to separate from her? And what are her rights if separation is necessary?

You are not required to separate from your wife if she repents with sincere repentance, for "repentance erases what came before it." You should complete the marriage and help her obey Allah. If you divorce her, she has the rights of a divorced woman with whom consummation has occurred, because the lawful privacy (khalwa shar'iyya) takes the place of consummation.