Short answers, pulled from the story.
Jean Poquelin was born in Paris shortly before his christening on the 15th of January 1622. A maid who saw him for the first time exclaimed Le nez, a reference to the infant's large nose, so his family called him Le Nez from that moment forward.
Molière likely changed his name to spare his father the shame of having an actor in the family after spending 24 hours in prison following the bankruptcy of the Illustre Théâtre in 1645. He began to use the pseudonym Molière at this time because actors were still not allowed to be buried in sacred ground.
Tartuffe, ou L'Imposteur was performed at Versailles in 1664 but created the greatest scandal of Molière's artistic career due to its depiction of hypocrisy. The play was banned by Lamoignon and the archbishop as soon as the King left Paris for a tour until the King finally imposed respect for Tartuffe a few years later.
Molière collapsed on stage during a fit of coughing and haemorrhaging while performing Le Malade imaginaire on the 17th of February 1673 and died a few hours later without receiving the last rites. The superstition that green brings bad luck to actors is said to originate from the colour of the clothing he wore at the time of death.
Many words or phrases introduced in his plays are still used in current French including tartuffe which means a hypocrite and harpagon named after the main character of The Miser who is an obsessively greedy man. The phrase galère means a difficult and chaotic situation derived from Les Fourberies de Scapin.