The main reason the European Age of Discovery got kicked off was the fall of Constantinople in 1453. With that, what tenuous European access that still remained to the Orient through Asia was cut off, for good more or less.
While Portugal had blazed paths around the Horn of Africa and established colonies and outposts all the way down Africa and in India, the trip around the Horn was perilous to the extreme. Common understanding of the size of the world at that time had it being much smaller than it actually was and Columbus thought it would actually be shorter to sail across the Atlantic to the Orient. He found North American right about where his calculations told him the Indies would be.
As for cruelty to the Indians, yes, the Spaniards were very concerned about it. The first stated purpose of their exploration was to bring Christ to the world. So, if their people were too cruel, then it was frowned upon. Granted, their standards of what was cruel and not cruel differed from ours today, but once one understands the logic of the time, you discover that there very definitely were rules. For instance, for all the wealth he brought to Spain, Cortez could never quite make it to respectability back home because of his humble origins and the brutality with which he dealt with the Mexicans.
