بسم اللہ الرحمن الرحیم

الجواب وباللہ التوفیق

1. If the physical/visible impurity was removed (نجاست حقیقہ) from the body by water, then that washed down water will in fact be impure water. Therefore, if it wets any part of the body or cloth, it becomes necessary to purify that part of the body or the part of cloth it had affected. 

2. If the Ritual Impurity Invisible impurity (نجاستِ حکمیہ) was removed, i.e., the impurity was not on the body, but “Wudu” or “Ghusl” was required to remove that type of impurity. Then water used to perform ablution or bath can be termed as “used water” which is pure, If it touches the clothes or the body, they do not become impure.  

   Now answers to your specific questions:

1. If impurity is washed from the body, then after washing, that water becomes impure.

2. After washing an impure carpet or floor or sofa, its water also becomes impure.

3. If after washing yourself, an impurity appears on the hand and its effects are visible, then the hand becomes impure.

4. If the hand is clean, the clothes held by it will also remain clean. But if the hand is unclean and impure and the clothes are grabbed by it and the hand's moistness touches them, the clothes will also become impure. 

5. At the place where impure clothes are hung, if both the clothes and the hanger are dry, the place will remain clean. The impurity of the clothes will not transfer to make that place impure. 

6. Praying with a little cut or tear on the clothes will make the prayer complete, but one should be careful not to wear clothes that are torn at the place of “sitr – the private parts” for prayer. Rather, one should arrange to put on the best available clothes for prayers. 

7. This is an illusion, do not pay attention to it. Obsessions usually involve demonic influences; so that a believer cannot perform purification and worship with satisfaction. It should not cause any worries. The remedy for these kinds of distractions is to not pay attention to it at all. 

In Summary:

a. Cleaning and purification of the body and clothes should be maintained.

b. Enter the toilet with the left foot first after reciting special duaa.

c. Do not spend time in the toilet more than what is necessary.

d. At the thoughts of impurity, recite the following:

أَعُوْذُ بِاللّٰهِ مِنَ الشَّیْطٰنِ الرَّجِیْمِ." ، لا حول ولا قوۃ الا باللہ العلی العظیم

And recite Surah "An-Naas" frequently.

أما المیاہ علی خمسۃ أقسامٍ: طاہرٌ مطہرٌ غیر مکروہٍ: وہو الماء المطلق۔ وطاہرٌ مطہرٌ مکروہٌ: فہو ما شرب منہ الہرۃ ونحوہ وکان قلیلاً۔ وطاہرٌ غیر مطہرٍ: وہو ما استعمل لرفع حدث أو لقربۃٍ الخ۔ والرابع: مائٌ نجسٌ: وہو الذی حلت فیہ نجاسۃٌ الخ۔ والخامس: مائٌ مشکوکٌ فی طہوریتہٖ، وہو ما شرب منہ حمار أو بغلٌ۔ (مراقی الفلاح ۸-۱۱)

 يَا بَنِي آدَمَ خُذُوا زِينَتَكُمْ عِنْدَ كُلِّ مَسْجِدٍ(الاعراف: ۳۱)

''منہاالغسل یجوز تطہیرالنجاسة بالماء وبکل مائع طاہریمکن ازالتہا بہ کالخل وماء الورد ونحوہ…ومن المائعات الماء المستعمل وہذاقول محمد وروایة عن ابی حنیفة وعلیہ الفتویٰ ہکذافی الزاہدی ''…(فتاویٰ الہندیة: ٤١/١)

''اماالماء المستعمل وعند محمد  و ہی روایة عن أبی حنیفة  أیضا ہی طاہر غیر طھور أی غیر مطھر و بہ أخذ أکثر المشائخ و ہو ظاہر الروایة و علیہ الفتویٰ''…(حلبی کبیری :١٣١)

فقط واللہ اعلم بالصواب