Is it permissible to wash the body with water and soap during the day of Ramadan? Does having a wet dream invalidate Sawm (Fast)? Also, does applying perfume invalidate Sawm?

Firstly: It is permissible for the fasting person to wash their body during the day of Ramadan with water and soap. Secondly: If someone has a wet dream during the day of Ramadan while fasting, this does not invalidate their Sawm; but they should perform Ghusl (ritual bath following major ritual impurity) if Maniy (sperm/vaginal secretions) is ejaculated. Thirdly: Sawm is not invalidated by applying any kind of perfume during the day of Ramadan while fasting, but one should not inhale incense or powdered perfumes such as musk.

May Allah grant us success! May peace and blessings be upon our Prophet Muhammad, his family, and Companions!