What should I do upon discovering that my wife had multiple illicit relationships (including physical encounters, explicit online chats, and sending photos and videos) with many young men before and after our engagement, despite her claiming repentance and remorse, and should I continue with her?

Correct repentance erases what came before it, and one who repents from a sin is like one who never sinned. If your wife has repented from her past actions and nothing suspicious has appeared from her currently, then you must conceal her faults, treat her kindly, and not pay attention to the whisperings of Satan. You must fulfill your role of guardianship over her, close the doors to temptations, establish God's limits in your home, and cooperate with her in obeying God, while having a good opinion of her. This is a protection from what is unlawful, a safeguard from temptations, and a way to cut off the paths of Satan.