What is the ruling on the dowry that was paid to the fiancée after the marriage contract, and is she entitled to half of it if it became apparent to the suitor after the contract that his fiancée had previous relationships and engaged in immoral acts, and he was unaware of this until after the contract?

Married life is a long journey that requires careful consideration when choosing a spouse. You might ask about a girl, and your family may praise her based on their knowledge. However, if a problem arises, consider her current situation and disregard the past, for errors and sins are human nature, and "all children of Adam err, and the best of those who err are those who repent." If she has repented, become righteous, improved her conduct, and you desire the continuation of the companionship, then hold onto her. You do not have the right to question her about her past, nor is it permissible for her to inform you of what happened, for her duty is to repent and conceal herself. If you separate from her, she is entitled to the dowry because you had a valid private seclusion with her.