Is it permissible for a married woman whose husband has not yet consummated the marriage to speak with him online late at night without the knowledge of her father, who disapproves of this?

Since you have entered into a marriage contract with this young man, you are his wife according to Islamic law, and what is permissible between spouses is permissible for both of you. You are not obligated to obey your husband until he hands over your immediate dower. At that point, obedience to your parents takes precedence over obedience to your husband.

If the internet belongs to your father and he forbids you from using it, then it is not permissible for you to use it without his permission. If your father dislikes your speaking with your husband before consummation, then obedience to your father takes precedence over obedience to your husband. However, there is no harm in combining fulfilling your husband's desire to speak with avoiding displeasing your father by concealing your conversations from him. If this is not possible, then avoid displeasing your father.