The goals of Hernan Cortez were to conquer the new lands, and to spread Christianity. He left Europe with a priest and a crew, and got to Central America. Instead of exclusively exploring he fought with the Aztec, end after killing a large amount of them he conquered the land that we now consider Mexico.
The Spanish government in the Americas changed very often, and was split between multiple governing parties. It was originally governed by the politicians in buenos aires, but since it took so long to get information they moved to a more independent system which eventually caused a revolution.
The Spanish had a very strict class system that showed where you were in society and what you could do as a job. The highest class, the peninsulares, were born in Spain and came to the Americas, the second highest were the Creoles which were of European descent but were born in the colonies. The mestizos were people of half European and have native descent, and on the same level were the mulattoes which were of African and European descent. The lowest level of people were those of African descent and Native descent.
The Portuguese showed interest in Brazil's sugar plantations and mostly Brazilwood, which provided a rich red dye, used for the coloring of textiles and clothing. They brought positive impacts on the Portuguese economy. The Portuguese king allowed private investors and colonists to settle on their own risk.
English first had a peaceful relationship with the native americans, after a while the relationship started shaking and started to have major conflicts with the native americans. The French came to America mainly for the fur trade, so they didn't try too hard to convert the Indians to Catholicism. During the French-Indian war, most of the Native American population was on the French side, because the French treated them better.
Treaty of Tordesillas was a treaty between Portuguese Empire and Spanish Empire that divided the newly discovered lands. It was signed at Tordesillas, on 7 June 1494 after the Colombus's discovery of America. It was agreed that the lands to the east would belong to Portugal and the lands to the west to Spain.