Is it obligatory to repeat prayers that were performed facing a direction other than the Qiblah? And if repetition is obligatory, should the missed prayers be made up in their daily order, or is it permissible to make up Fajr prayers, for example, with the current Fajr prayer? And is it necessary, when intending to make up a prayer, to specify the obligatory prayer along with its day?

The validity of your prayers for a week, facing a direction other than the Qiblah, depends on your diligence. If you made an effort and erred, your prayers are valid, and there is nothing upon you. However, if you were negligent and did not make an effort, or if you made an effort in an inappropriate situation, then you must repeat those prayers. You should hasten to perform them in order, day by day, to the best of your ability. When making up prayers, it is not necessary to consciously state the intention of "making up" or "performing"; rather, it is sufficient to intend that these prayers are for those days, specifying the prayer (Dhuhr, Asr, Maghrib), without needing to specify the day (Thursday, Friday). It is sufficient to perform prayers for a number of days equal to the number of days you prayed facing a direction other than the Qiblah.