Is it permissible to pray the obligatory prayer in an airplane or car, while sitting in a seat and not facing the Qiblah?

Standing during obligatory prayers is a pillar that is not waived except in case of inability. Facing the Qibla (definition) is an obligation. Therefore, prayer in a car, while sitting or not facing the Qibla, is not valid. Rather, one must dismount and pray standing, facing the Qibla.

In an airplane, one must pray standing and facing the Qibla if possible. Otherwise, one should pray standing in their seat. If unable to do so, then pray sitting.

If there is ample time before the prayer's due time expires, it is preferable to delay the prayer until landing, unless there is a place to perform the prayer fully on the plane.

If one fears that the time will expire, they should combine the prayer with the subsequent one through a delayed combination (jama' ta'kheer) if it is among the prayers that can be combined. Otherwise, they should pray on the plane according to their ability, standing and facing the Qibla, performing bowing (ruku') and prostration (sujud (definition)) if possible, and otherwise gesturing (ima').

As for public places in lands of disbelief, merely living there does not permit abandoning standing (qiyam (definition)). Neither mockery nor shyness is an excuse for abandoning standing in prayer. The entire Earth is a mosque, and whoever abandons standing without an excuse, their prayer is invalid.

If there is a legitimate Sharia (definition)-compliant reason for not praying openly, such as fearing harm, then one should delay the prayer until reaching home or the mosque. If one fears the time will expire along with fearing harm, then there is no harm in praying sitting out of necessity.