Meaning of shahaadah

Q:

1. Some say that actually saying the shahaadah is not required to be considered a Muslim and rather just to actually believe in your heart while others say that you have to actually say the shahaadah, which is correct?

2. Why does the Hanafi madhab believe that despite not praying, as long as they believe in the shahaadah's message, people can still be considered Muslim and eventually enter paradise. If it is said that the Prophet (sallallahu alaihi wasallam)'s uncle believed that his nephew was not lying and telling the truth yet will enter hell? Is it because he refused to say the shahaadah, regardless of whats in his heart?

Are dog hairs impure?

Q: I travel for work and sometimes my agent takes me around in his vehicle. There are times when his vehicle has some dog hair on the seats and on the floor. By me sitting on the seat, some of the hair may come onto my clothes which I try and remove. Can I read salaah or are my clothes napaak?