Is the prayer considered valid if the Qibla direction was determined using a compass, despite doubt about the accuracy of the direction, and is it permissible to shorten prayers for a Muslim who is traveling most of the time?

If someone is far from the Kaaba and prays in its direction, and they are fairly certain that the Qibla is in the direction they are facing, their prayer is valid. So, as long as you have exerted effort and used a compass to determine the direction of the Qibla, pray in that direction and do not pay attention to doubts; they are from Satan. It is permissible to shorten the four-rak'ah prayers and combine the prayers that share a time (Dhuhr with Asr, and Maghrib with Isha) during permissible travel, provided that you intend to travel a distance of not less than 83 km.