What is the ruling on performing ablution (Wudu') and ritual bathing (Ghusl) with usurped water, which was obtained and heated with usurped electricity and gas? And is the prayer valid for a woman who applied perfume and was smelled by men?

If the water is usurped, the majority of jurists hold that purification is valid though sinful, while the Hanbalis consider it invalid. The preponderant opinion is that it is valid, though sinful, and the water must be guaranteed to its owner. However, if what was used to heat the water (such as electricity or gas) was usurped, purification is valid though sinful. It is disliked to perform ablution with water heated by usurped means. As for a woman who applies perfume and men smell it, her prayer is valid though sinful.