How can the end times for the Asr and Maghrib prayers be determined if it is not possible to rely on the sun and shadow? Is there a maximum or minimum time limit for the prayer? And is attending private lessons considered an excuse for delaying the Asr prayer until the time of necessity?

The time for the Asr prayer begins when the shadow of an object becomes equal to its height, and it ends with the sunset, which is the time of Maghrib.

There are two periods for the Asr prayer: an optimal time (waqt ikhtiyar) that extends until the sun turns yellow, and a time of necessity (waqt dharurah) that extends until sunset.

It is not permissible to intentionally delay the prayer until the time of necessity unless there is a valid excuse.

The questioner can attend the lesson while having wudu and then seek permission to pray before the optimal time (waqt ikhtiyar) expires.

If she is unable to pray during the optimal time due to an excuse, there is no sin upon her for praying during the time of necessity, and her prayer will be considered performed on time (ada'an).

One can rely on trustworthy calendars to determine prayer times.