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?

Following the Jamaat Salaah of the Haram from the Hotel Jamaat Khaana

Q: Nowadays, some people are performing salaah in the hotel near the Musjid al Haraam while following the jamaat of Musjid al Haraam. The hotel has speakers installed and the recitation of the Imaam of Musjid al Haraam can easily be heard. However, since the Imaam is not present infront of the muqtadis, I am doubting whether the salaah is valid or not. Is it permissible for people to follow the Imaam in salaah while in their hotel rooms? Similarly, is it permissible to follow the Imaam in the hotel jamaat khaana?