Is it permissible to fast Mondays and Thursdays, and the White Days (13th, 14th, 15th) while performing 'Umrah?

There is no harm in fasting while traveling for 'Umrah if it does not cause harm to the fasting person, based on the saying of the Prophet (peace be upon him): "If you wish, fast, and if you wish, break your fast."

However, if the fasting person is harmed or weakened to the extent that they cannot perform the rituals and acts of worship, such as the circumambulation (Tawaf), then it is better for them to break their fast, based on the saying of the Prophet (peace be upon him): "It is not righteousness to fast during travel," which applies specifically to those for whom fasting is burdensome and harmful.

Engaging in Tawaf and prayer in the Grand Mosque is more virtuous, as a single prayer there is equivalent to one hundred thousand prayers, and Tawaf is an act of worship exclusive to it. If fasting weakens one from performing these virtuous acts of worship, then engaging in fasting would be prioritizing a less virtuous act over a more virtuous one.