Is it permissible for me to perform dry ablution instead of the ritual purificatory bath so that I can perform the Fajr prayer on time, out of fear of becoming ill, before its prescribed time ends? When I perform the ritual purificatory bath before the Dhuhr prayer, should I repeat the Fajr prayer, given that I am prone to catching colds and cannot sleep after bathing because of the cold?

There is no objection to performing dry ablution (tayammum) instead of the ritual purificatory bath if a person fears becoming ill to the extent that they would be unable to use water, or if using water would worsen their illness or delay their recovery. The inquirer is not required to repeat the prayer.

And Allah Almighty knows best.