Short answers, pulled from the story.
The Paris Peace Conference formally opened on the 18th of January 1919 at the Quai d'Orsay in Paris. The formal peace process did not fully conclude until the 24th of July 1923, when the Treaty of Lausanne was signed, although the senior statesmen stopped working personally on the conference in June 1919.
The five treaties were the Treaty of Versailles with Germany on the 28th of June 1919, the Treaty of Saint-Germain with Austria on the 10th of September 1919, the Treaty of Neuilly with Bulgaria on the 27th of November 1919, the Treaty of Trianon with Hungary on the 4th of June 1920, and the Treaty of Sevres with the Ottoman Empire on the 10th of August 1920, which was later revised by the Treaty of Lausanne.
The Big Four were French prime minister Georges Clemenceau, British prime minister David Lloyd George, US president Woodrow Wilson, and Italian prime minister Vittorio Emanuele Orlando. Together with their diplomatic teams they met informally 145 times and agreed upon all major decisions before those decisions were ratified.
China refused to sign because Article 156 of the treaty transferred German concessions in Jiaozhou Bay to Japan rather than returning sovereign authority to China. The delegation's leader, Lu Zhengxiang, demanded a reservation be inserted before signing, and when that was denied, China became the only delegation not to sign at the signing ceremony. The decision triggered widespread student protests in China on the 4th of May 1919, known as the May Fourth Movement.
The Racial Equality Proposal was introduced by the Japanese delegation on the 13th of February 1919. It sought to add a clause to the League of Nations Covenant guaranteeing equal and just treatment regardless of race or nationality. Wilson ruled as conference chairman that a unanimous vote was required, and although 11 of 17 delegates voted in favor, Britain abstained under pressure from Australia and South Africa, causing the proposal to fail.
No. The United States Senate never ratified any of the five peace treaties, so the United States never joined the League of Nations. Opposition centered on Article 10 of the League's Covenant, led by Senator Henry Cabot Lodge. The Harding administration instead concluded separate treaties with Germany, Austria, and Hungary between 1921 and 1923.