What is the meaning of the visions and achievements, and the loyalty of Thair and Tamer?

The vision (Ru'ya): What a sleeping person sees in their sleep; its plural is visions (Ru'a).

The gain/attainment (Manal): The giving/granting.

The loyalty/allegiance (Wala'): From showing allegiance (Muwalat), the opposite of showing enmity (Mu'adat), or from continuous succession (Tawali) and sequence.

The enraged/rebellious (Tha'ir): The angry, agitated one.

Tamer (Tamer): Owner of dates, or one who feeds dates.