Short answers, pulled from the story.
The Sanskrit compound Ganesha joins gana, meaning group or multitude, with isha, meaning lord or master to create the title Lord of Hosts. This construction establishes him as the Lord of Created Categories in Hindu theology.
Archaeological finds from Ter, Pal, Verrapuram, and Chandraketugarh reveal small terracotta images dating to the 1st century CE. These early figures possess an elephant head but only two arms and an endomorphic physique before stone carvings emerged during Kushan times between the 2nd and 3rd centuries CE.
Puranic texts composed after 600 CE describe how Parvati created Ganesha from clay to guard her privacy when Shiva returned and tried to enter. The boy blocked his path and was beheaded before Shiva replaced the severed head with that of an elephant.
Lokmanya Tilak transformed this private celebration into a grand public event in 1893 to foster grassroots unity against British rule. He installed large images in pavilions and established submerging all public statues on the final day to create huge proportions in Mumbai, Pune, and surrounding areas.
Statues appear throughout Java, Bali, Borneo, Burma, Cambodia, and Thailand with specific regional influences following commercial contacts extending India's influence from approximately the 10th century onwards. An inscription dated 531 marks the earliest known stone statue in northern China while Japan mentions the cult in 806 under the name Kangiten.