What is meant by the disagreement among scholars regarding the imamate of the fasiq (openly disobedient/wicked person): Is it concerning his leading the prayer or his leadership as a ruler (Wali al-Amr)? And how can a prayer be disliked (makruh) and then described as invalid (la tasih)?

The Shaykh's words concern the imamate of prayer, not the Grand Imamate (caliphate). There is no contradiction between his mention of the scholars' consensus on its reprehensibility (karahah) and his نقل (narration) of some scholars' view that it is invalid. His intention is that some scholars consider it to be tahrimi karahah (prohibitive reprehensibility) and invalidate prayer behind a fasiq (transgressor), while others consider it tanzihi karahah (disapproving reprehensibility). No scholar has ever said that leading prayer as a fasiq is permissible and equally valid.