Water is a transparent, tasteless, odorless, and nearly colorless chemical substance, which is the main constituent of Earth's streams, lakes, and oceans, and the fluids of most living organisms. It is vital for all known forms of life, even though it provides no calories or organic nutrients.
If the washing machine is connected to the tab water, then it will be Taahir along with all the clothes inside it. If there is no connection with tab water or any Kurr water, and water used is less than Kurr, then Najis cloth will remain Najis unless it is washed and rinsed twice with Taahir water.
Every solid item can be purified (Taahir) with water if it was not Taahir. Plastic utensils are no exception.
You can perform Wudhu just before starting your shower. It can be also done after shower but after you dry your head and feet where wiping on them is compulsory.
As far as it helps the public health, and does not harm people, then it is allowed and it might be recommended or even compulsory if the water is the aea is not suitable for drinking and it might harm public health before fluoridation. Obviously the percentage of the fluoride must be accurate.
Yes your fast is valid.
If you have doubt as to whether there was something obstructing water from reaching your skin or not, after having performed the ghusl, you consider the ghusl as valid.
However, if you are sure it was there before the ghusl, and forgot during the ghusl, and then realised after the ghusl that it the obstruct was there, then as long as you kept your taharah, wash that part, based on the ruling of tarteeb (sequence).
And Allah knows best.
If a person who is fasting eats or drinks by mistake, and not intentionally his fast is in order.