Tahaarat

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?

Seeing discharge upon awakening

Q: If a woman who always suffers from vaginal discharge which is continuous throughout the day and night. Sometimes the discharge has a foul odor and it is thick white like leucorrhoea and sometimes the white discharge has mild odour or no odour.

After waking up, if she finds the white discharge with a foul odour and she is certain that she did not have a wet dream, does ghusl become compulsory?

Note: She is very certain that she didn't have any wet dream.