Is it permissible for a suitor to visit his fiancée at her family's home and speak with her in their presence without a valid Islamic marriage contract, and does this entail any prohibition?

The fiancée is a stranger to the suitor. Therefore, it is not permissible to be alone with her or to speak with her except out of necessity. It is permissible to go to her home to negotiate with her father, visit them, and communicate with them. The family's refusal to allow her to be visited until the marriage contract is concluded is a sound opinion. You can conclude a legal marriage contract with her and await the end of her exams to hold the wedding feast. By doing so, she becomes your wife, and it becomes permissible for you to be alone with her.