Is uncovering the head outside of prayer considered an imitation of the disbelievers, as Al-Albani stated, and what did the Prophet and the Companions wear on their heads, and is it confirmed that any of them were bareheaded, and did the Prophet wear the white or red ghutra that Ibn Baz used to wear, and what did he wear over his thobe?

There is no objection to wearing a cap during prayer or outside of it, unless it is part of the attire of the disbelievers, as mentioned in the Hadith of Ibn Umar. The Companions used to wear turbans and skullcaps as an emulation of him. We have no knowledge of what the Prophet, peace and blessings be upon him, wore over his garment, nor is there any resemblance between that and what العلامة ابن باز (scholar Ibn Baz) used to wear.