Is intercourse permissible between a husband and wife after the marriage contract (Aqd Al-Qiran) but before the wedding celebration (Al-Farah), if the wife has received her dowry (mahr)? And will the doer be held accountable for that in Islamic law?

Your wife became permissible to you through the legitimate contract, and all that is permissible for a husband with his wife became permissible for you with her. You did not commit a sin by having intercourse with her. However, it is not preferred to have intercourse with the wife before the official consummation, out of consideration for customs, so that it does not open a door for Satan and cause problems. As long as you have paid your wife's mahr (dowry), her family must hand her over to you, and they are not allowed to refuse unless there is a valid reason, such as stipulating a delay of a year due to the wife's young age or her absence.