Short answers, pulled from the story.
The Shakyas were an ancient Indo-Aryan tribe of north-eastern South Asia whose existence is attested during the Iron Age. They lived in the Terai, the strip of land south of the Himalayan foothills and north of the Indo-Gangetic Plain, with their capital at Kapilavastu. Their neighbours included the Kingdom of Kosala to the west and south, the Koliya tribe across the Rohini River to the east, and the Mallakas of Kushinagar to the northeast.
The Shakyas were organised as a gaṇasaṅgha, an aristocratic oligarchic republic. An Assembly of aristocratic rājās met in a santhāgāra or assembly hall at Kapilavatthu, with a smaller inner Council of amaccās handling day-to-day administration. The head of the republic held the title of mahārājā, an elected position of first among equals comparable to a Roman consul or Greek archon. Voting was conducted by raised hands or the use of wooden chips.
Yes. Siddhartha Gautama, the historical Buddha and founder of Buddhism, was born into the ruling aristocratic oligarchy of the Shakyas. His father Suddhodana was a member of that ruling class, and his mother Māyā was the daughter of a Koliya noble. His followers gave him the epithet Sakka-muni in Pali and Śākya-muni in Sanskrit, meaning Sage of the Shakyas.
The Shakyas followed non-Vedic religious customs rooted in the Greater Magadha cultural tradition. They worshipped the Sun-god as their divine ancestor, practised tree worship centred on the Sāl tree, venerated tree spirits called yakkhas and yakkhīs, and observed serpent worship associated with pre-Indo-Aryan Tibeto-Burman traditions of northern South Asia. Brahmanism had not acquired religious or cultural dominance in their region even by the time of the Buddha.
The Kauśalya king Viḍūḍabha, who had overthrown his father Pasenadi, invaded the Shakya and Koliya republics shortly after the Buddha's death and annexed them after a long war with massive losses on both sides. The Shakyas subsequently disappeared as an ethnic group, absorbed into the population of Kosala. The heavy losses Kosala sustained during this conquest then left it vulnerable, and the Kingdom of Magadha under Ajātasattu annexed Kosala and killed Viḍūḍabha.
The Tharu people of the Terai region of India and Nepal claim descent from the Sakya. Significant populations of Newars in the Kathmandu Valley of Nepal use the surname Shakya and claim descent from the Shakya clan, with the historical title Śākyavamsa, meaning "of the Shakya lineage," recorded in their traditions. According to Hmannan Yazawin, first published in 1823, the legendary king Abhiyaza, who founded the Tagaung Kingdom and the Burmese monarchy, was also said to belong to the Shakya clan.