Short answers, pulled from the story.
The Kuomintang traces its origins to the 24th of November 1894, when Sun Yat-sen founded the Revive China Society in Honolulu, the capital of the Republic of Hawaii. The party was reconstituted under its current name on the 10th of October 1919 in Shanghai.
Sun Yat-sen's Three Principles of the People are nationalism, democracy, and people's livelihood (Minsheng). Sun defined Minsheng as socialism, drawing on the ideas of American thinker Henry George, and called for nationalized railroads, utilities, and state control of land and mineral income to fund social welfare programs.
The White Terror was a KMT-led political repression that followed the February 28 Incident of 1947. It resulted in the death or disappearance of over 30,000 Taiwanese intellectuals, activists, and people suspected of opposing the KMT. Martial law remained in effect until 1987.
The KMT lost because of compounding failures: drastic troop reductions after Japan's surrender that pushed trained soldiers toward the PLA, uncontrolled hyperinflation, a failed currency conversion in August 1948 that left the Gold Standard Scrip worthless within ten months, urban-focused military strategy that ceded the countryside, and widespread corruption that alienated the public and strained relations with the United States.
The KMT opposes formal Taiwan independence and opposes unification under the PRC's "one country, two systems" framework. It accepts the 1992 Consensus, which defines both sides of the Taiwan Strait as "one China" while leaving the interpretation ambiguous, and advocates maintaining Taiwan's current status quo while pursuing closer ties with Beijing.
The KMT once accumulated assets estimated at between US$2 billion and US$10 billion, making it what was believed to be the world's richest political party. In July 2014, it reported total assets of NT$26.8 billion. After the DPP won power in 2016, the Ill-gotten Party Assets Settlement Committee was established to investigate and recover assets acquired during the martial law era.