Their colonial experience led them to the point where they were sick of monarchistic European influence and wanted to create a fully democratic republic, created by the people for the people, not for the well being of a royal family.
People believed that the Earth was actually the center of the universe, and he was concerned about publishing his ideas because this was very frowned upon and he would get harshly critcized and most likely punished for this idea.
In the 15th and 16th centuries, Europeans wanted to find sea routes to the Far west. Columbus wanted to find a new route to India, China, Japan and the Spice Islands. If he could reach these lands, he would be able to bring back rich cargoes of silks and spices.