Is it permissible to supplicate for the deceased from inside the car after entering the cemetery and greeting them with the traditional supplication without facing the Qiblah?

There is no impediment to supplicating for the deceased when you are not facing the Qibla, and there is no evidence to prohibit that. However, it is recommended to face the Qibla when supplicating, as it is among the general etiquettes of supplication.