Can a young man file a lawsuit against the family of the girl he was engaged to, and they agreed to the engagement on the condition that she complete her studies, then he was surprised by her engagement to another person without being informed, and is her marriage valid or void?

It is unanimously forbidden for a man to propose to a woman who is already engaged to another, after both parties have agreed and are content with each other. If the new suitor is aware of that engagement, he is sinful. The consent of the girl's family to your marriage is a covenant that should not be broken except for a legitimate Shar'i reason. However, this marriage that took place is a valid marriage.

There is not much benefit in litigation unless you have financial rights against the girl (money you spent or a gift), in which case you are permitted to demand it. Counting these matters with Allah is better, for Allah will compensate you. Forget about this girl, for perhaps Allah has averted evil from you, or has reserved good for you in marrying someone else. Remember the words of Allah Almighty: (And it may be that you dislike a thing which is good for you and that you like a thing which is bad for you. Allah knows but you do not know).