Short answers, pulled from the story.
Ratnagotravibhaga translates as "Analysis of the Jeweled Lineage" or "Investigating the Jewel Disposition." The Sanskrit ratna means jewel, and gotra refers to innate spiritual disposition or family lineage. The title points to the text's central argument that the disposition allowing all beings to become Buddhas is itself precious, like a jewel.
Authorship of the Ratnagotravibhaga is disputed. Chinese tradition, traceable to the sixth-century scholar Zhiyi, attributes it to an Indian named Sāramati (c. 3rd-4th century CE). Tibetan tradition attributes the verse portion to the bodhisattva Maitreya and the commentary to Asanga. Modern scholarship largely favors the Chinese attribution to Sāramati.
The RGVV was likely composed between the middle of the third century and no later than 433 CE. A Sanskrit copy was brought to China by Ratnamati in 508 CE and translated at Luoyang in 511 CE, establishing that the complete text existed in India by the early sixth century.
The Ratnagotravibhaga teaches that all sentient beings possess buddha-nature (buddhagarbha or tathāgatagarbha), describing it as permanent, blissful, unconditioned, and originally pure. This nature is obscured by defilements but remains unchanged by them. When defilements are removed, buddha-nature is termed the dharmakaya, the ultimate Buddha body.
The Ratnagotravibhaga presents its buddha-nature teaching as the final and highest (uttara) teaching of the Mahayana, which it claims both includes and goes beyond the earlier Prajñāpāramitā emptiness sutras. RGV verses I.157-158 state that buddha-nature is empty of adventitious stains but not empty of its own unsurpassable qualities - a formulation that distinguishes it from a pure negation.
The seven vajra points or adamantine topics of the RGV are: the Buddha, the Dharma, the Sangha, the dhātu (buddha-nature), bodhi (awakening), the buddha qualities, and Buddha activity. RGV verse I.3 explains that from the Buddha comes the Dharma, from the Dharma the Sangha, and within the Sangha the tathāgata heart leads to the attainment of wisdom and supreme awakening.