How sound is Abu Dawud’s hadith, "He would point with his finger and not move it," and is the addition "and not move it" of sound and established isnad, and does it contradict Wa’il ibn Hujr’s hadith, "He would move it, supplicating with it," and how can the two be reconciled?

The hadith you inquired about has a sound chain of narration (saheeh isnad), including the phrase: "he does not move it," and this does not contradict the hadith of Wa'il ibn Hujr. Some scholars have gone to the extent of saying that the meaning of moving the finger is to point with it without continuously moving it. Imam Al-Nawawi said in Al-Majmoo': "It is recommended to move it," citing as evidence the hadith of Wa'il ibn Hujr: "Then he raised his finger and I saw him moving it, supplicating with it." Al-Bayhaqi said: "It is possible that the meaning of pointing with it is not to repeatedly move it." As for Ibn Al-Zubair, it was narrated from him that the Prophet (peace be upon him) "used to point with his finger when he supplicated, not moving it." In Al-Sharh Al-Mumti' by Sheikh Ibn 'Uthaymeen, the Sunnah indicates that one points with it only when supplicating, and that the negation of movement refers to continuous movement, while the affirmation of movement refers to movement during supplication.