Is it obligatory for a Muslim to follow a specific school of thought (madhhab), and what is the evidence for that? Can a Muslim adopt rulings from different sources if they do not follow a specific school of thought, or must they adhere to one source?

Affiliation with a particular madhhab (school of thought) or sect is not obligatory. Rather, what is obligatory is to follow the Book of Allah and the Sunnah of His Prophet (peace be upon him) according to the understanding of the noble Companions, whom Allah and His Messenger have praised. After that, one may seek illumination from the words of the imams and scholars who follow this methodology. There is no harm for the layperson who cannot weigh evidence to follow whichever madhhab he wishes, so long as that is not a pursuit of personal whims.