Is the hadith, "Whoever speaks about the Qur'an according to his own opinion and errs, has disbelieved," authentic? And does disbelief apply to someone who interprets the Qur'an incorrectly out of ignorance?

No hadith with this exact wording has been found, but texts prohibiting speaking about the Quran without knowledge have been narrated, such as: "Whoever speaks about the Quran by his own opinion, let him take his seat in Hellfire," and "Whoever speaks about the Quran by his own opinion and is correct, has erred." This means that whoever interprets the Quran without a legal or rational proof consistent with the Sharia has erred, even if he arrived at the correct meaning, because he did not approach the matter through its proper channel.