Are the whispers and thoughts that a person experiences, including questioning the validity of the creed and the multiplicity of hadiths, considered disbelief (kufr)? What should he do, and is it forbidden to ask these questions?

The cure for waswasah (whisperings/obsessive thoughts) is to seek refuge in Allah, to desist from them, and not to pay them any attention. Asking people of knowledge when ignorant is required, and it is a cure for ignorance. However, it is not permissible to persist in asking questions without accepting the answer or to reject religious texts under the pretext of intellect, for that is one of the gateways to destructive fitan (trials/temptations). Disagreement is a breadth and a mercy if it is in matters of ijtihad (independent reasoning) that do not contradict a text and do not violate a consensus.