What is the ruling on a traveler's prayers that he combined and shortened, without knowing the duration of his stay, or knowing it to be two days or less, and he prayed therein the Dhuhr with the Asr, by way of taqdim (combining earlier) and ta'khir (combining later), and the Asr with the Dhuhr, by way of taqdim and ta'khir, and in some instances he completed the prayer or joined the Imam in the third rak'ah?

In the first case (Dhuhr prayer after Asr prayer): If you were unaware of the necessity of the sequence, the majority of jurists believe that ignorance does not waive the requirement of sequencing. However, others, including Sheikh Ibn Uthaymeen, hold that an ignorant person is not harmed by neglecting the sequence, and their prayer is valid. Therefore, you are not required to repeat the Asr prayer, but repeating it as a precaution is good.

In the second, third, and fourth cases: If you shortened the prayer behind a resident Imam, your prayer is invalid, and you must repeat it in full, unshortened; because a traveler who prays behind a resident must complete the prayer. However, if you completed the prayer and did not shorten it, your prayer is valid.