Impurities

Are hair roots impure?

Q: Is the root of the hair najis? And if so, what does this really mean? Since the hair that the body has naturally shed has the root intact (as opposed to cut hair), do I then assume that all hair that I see on the floor or in the bathroom has a part of it that is najis?

As a consequence, if I am eating soup or drinking water, and some hair falls in, does that make the entire liquid najis? If some fallen hair on the floor sticks to my wet foot, do I have to wash my foot? How exactly is the najasat of the hair root transferred?

Washing an impure floor

Q: I saw urine on the floor so I was wiping it but did not finish it when someone stepped on it but at that time color of water was not like urine but I was not finished. After I finished the same person again stepped on the clean wet floor. Will the floor again become impure or not?

Not washing one's hands when waking up

Q: The one who wakes up, his hands are napak? What is the ruling for a person who does not wash his hands and goes to the washroom and touches the taps etc. and after washing his hands does not pour water on the taps and closes the tap. So does his hands, the taps etc. become napak? What about if he touches other things, will that also become napak? 

Rubbing impurity on the ground

Q: I ride scooters and bikes to school. I rolled over non-halal foods/sandwich packages with leftover foods several times when riding on the streets. I live in the U.S. and the sandwiches are subway wraps with wet food oil and sauce and certainly not halal. Hence, the bike tire becomes impure. When I ride it in rainy days, the water splashes from the tire onto my shoes and pants. Since the bike tire is impure the water splash is impure. I have to go back home and wash them every time I pray and it severely impacts my life. However, I heard that walking or rubbing impurity against the ground makes the impure shoe pure. Does this ruling apply to a bike/scooter tires? If so then the bike tire can be regarded as pure as it rubs against the ground so many times?