How is one to pray over a child who died from a harmful disease and was wrapped in polyethylene, making it impossible to wash or perform tayammum on him? And is one to pray over him without purification when washing and tayammum are not possible?

The basic principle is that washing a deceased Muslim is a communal obligation (fard kifaya). If washing is not possible, water should be poured over the body. If pouring water is also not possible, then tayammum (dry ablution) should be performed. If none of these are possible, the more likely opinion is that the funeral prayer should be performed over the deceased as is, without washing or tayammum. This is the view of Ibn Habib from the Maliki school, the Hanbalis, and some later Shafi'is, based on the hadith: "When I command you to do something, do as much of it as you can," and because the purpose of the prayer is to supplicate for the deceased. As for the Hanafis and the majority of Shafi'is and Malikis, they do not pray over the deceased due to the absence of the condition of washing or tayammum. Accordingly, it is permissible to pray over a child whose washing and tayammum were not possible.