And why are there so many more nation states in Africa?
Well one reason is that Africa is part of the Old World, and Africans had exposure to Old World diseases. If anything, diseases such as malaria is part of what made colonization of Africa difficult for Europeans. Native Americans by contrast were not exposed to diseases that were common in the Old World. It is estimated that millions, if not tens of millions, of them died in the decades after the arrival of Europeans. Thus the Americas were left quite depopulated of its native population.
The second reason is that American climate and geography was more favorable to European colonization.
To answer your second question, there are more nation states in Africa partly because of the result of decolonisation, and partly because of the effect of the US and its idea of Manifest Destiny. I'll take each continent one at a time.
In the case of Africa, you have a lot of European powers - England and France, especially - claiming land and colonising lots of different peoples without much regard for the borders that had existed previously and without concern for the ethnic and cultural groups there (here is a map that sort of illustrates what this looked like). The result of this is that when decolonisation came, people were divided not only along traditional lines (though to what extent there were "tribal" divisions varies depending on where in Africa you are), but also based on who colonised them and their experiences under colonisation. Equally, the colonial powers did also try to keep the areas that had been under their colonial control together, at least to a certain extent. That's why, for instance, the Portuguese area on that map lines up nicely with Angola. For political reasons (and for reasons of neo-colonialism), it made sense to keep colonies with a similar colonial background together, then divide them depending on the actual people living there. While it would be wrong to say that the Africans had no say in the matter, many of the borders were drawn during decolonisation, and were drawn with colonial histories in mind.
Compare that to South America, which didn't have anywhere near the same diversity of its colonial powers. Equally, it's worth noting that many South American nations gained independence before the period of decolonisation in the wake of WWII really kicked off. However, in that area, you find a lot more unity in terms of language, and thus not nearly as many small divisions based on who colonised what.
Then in Central America, you once again have one main colonial power (Spain). Because of this, things like the Constitution of 1812 had a massive effect, moreso than would be seen in any one document relating to decolonisation. Indeed, Napoleon's invasion of Spain allowed for a successful rebellion of the American colonies. This led to the First Mexican Empire, which united Central America for two years before collapsing. This then led to the Federal Republic of Central America, which contained many of the countries in modern Central America (except Mexico). These regions broke off and gained independence (I find it comparable to Yugoslavia) over the next few decades, breaking on cultural, linguistic, geographic, and sometimes ethnic boundaries.
Finally, there's North America, where we have a grand total of two nations. Canada and its very large unified-ness can be understood to be because of colonialism as well as its sparse population. In the case of the US, though, you have a federal system that makes it easy to integrate many different ideologies under one banner while keeping them all intact. Couple that with a narrative of "out of many, one" and the idea of Manifest Destiny, and it was possible for the US to expand and absorb in a way that colonial powers were able to do in Africa.
I hope that answers your question, and if not, feel free to ask more!