Is it permissible to combine two prayers due to light rain, or is it conditioned upon the rain falling at the time of intending to combine for the second prayer along with one's clothes getting wet? Is it a condition for the rain to be present during the prayer, or is it permissible to combine prayers throughout the entire week if it is a rainy week? And what is the madhhab of Sufyan al-Thawri on this issue?

What your friend said is a clear error, because the rain that permits joining prayers is that which wets clothes and causes hardship when going out in it. It is not permissible to join prayers for light rain that does not wet clothes. It is stipulated for the permissibility of joining prayers that the excuse exists at the beginning of the first prayer and continues until one starts the second, or even until finishing it. So, if one enters the Dhuhr prayer without rain, then rain comes, it is not permissible for him to join prayers. It is not permissible to join prayers where there is no excuse that permits it. The Hanafis absolutely forbid joining prayers in rain, while the majority of scholars permit it with the aforementioned conditions.