What is the remedy for misgivings about the authenticity of religious accounts, such as the reason for the revelation of Surat Al-Kahf, or Abu Lahab's secret conversion to Islam, and is it permissible to mention the chains of transmission (asanid) for these accounts?

The authenticity or weakness of an occasion of revelation (sabab an-nuzul) or the story of a particular man does not justify obsessive thoughts (waswasah), and you must treat the waswasah.

The occasion for the revelation of Surat Al-Kahf was narrated by exegetes from Ibn Ishaq, who received it from an unspecified شيخ (shaykh), which weakens its chain of narration (sanad). However, the story has a sound basis, as Imam Ahmad, At-Tirmidhi, Al-Hakim, and others transmitted with a sound chain of narration that Quraysh asked the Jews for something to test the Prophet, peace and blessings be upon him. They asked him about the soul, whereupon the verse from Al-Isra' was revealed: "And they ask you, [O Muhammad], about the soul..."

As for Abu Lahab, he did not embrace Islam, neither secretly nor openly. Scholars have considered his failure to embrace Islam among the proofs of prophethood, as it involved a future prediction that came true, thus indicating the truthfulness of the prophethood. Abu Lahab died from the disease of Al-'Adasah (a malignant pustule) seven nights after the incident where he was struck by Al-Abbas's servant.