Frank, it sounds like you have more than one issue here, first on the TX it sounds as if there is a short on it, it should not drain the batteries that fast and the leaking batt may be due to that
on the plane with 5 min flights, if your running nimh batts that is prob all your going to get with the 7V motor, they take more power to run than the 6V. Did you cycle your new batt, if not it will improve after a few cycles. I would go back with the 6V motor and call Hitech about the TX, you may can send it to them to repair. Don't give up and Good luck