Is hearing satanic whispers that cast doubt on the infallibility of Prophet Muhammad (peace be upon him) and the possibility of him committing sins considered disbelief or reviling the Prophet, and does that affect a Muslim's faith?

It is clear that the questioner is suffering from waswasah (whisperings/obsessive thoughts). She must completely ignore them and pay no attention to them. She should cast aside these illusions and thoughts, and occupy her mind with learning, inviting to Allah, and social services. She should not give Satan any way over her, nor should she imagine that she is dialoguing with him. Waswasah is a serious illness, and thinking about it and yielding to Satan will only strengthen its hold.