Is it obligatory to believe everything the Messenger, may Allah’s prayers and peace be upon him, conveyed in matters of religion without exception? What is the proof for that? And what about the Messenger’s, may Allah’s prayers and peace be upon him, error in his ijtihad regarding the matter of the captives?

Everything the Messenger, peace and blessings be upon him, said must be believed, as Allah the Almighty says: "Nor does he speak from [his own] inclination. It is not but a revelation revealed." Even if he were to exert his own reasoning in a matter and make a mistake - which is rare - Allah would not let him persist in it. Rather, revelation would descend to clarify what is correct.