Herp derp derp
a) No there weren't tropical diseases in Latin America, at least till later when they were transplanted from Africa. There's still massively less disease burden even to this day. Africa is where we evolved, and where everything knows how to kill us.
b) Europeans settled the Andes and a coastal strip of Brazil, neither of which are analogs to African environments. It took centuries to penetrate the interior of the tropical Americas, indeed you could argue they still haven't.
a) You say that most of the tropical diseases were transplanted from Africa to America. You got a point. It's inevitable, however, to all of them to reach America with the Columbian Exchange, they all came with the first European (and African) colonists to the new world. Yellow Fever, Malaria, Dengue Fever, etc. are just as epidemic in Africa that is in America nowadays. The fact they are much more deadly in Africa is just a matter of political issue.
b)
http://en.wikipedia.org/wiki/Brazil_Gold_Rush About 400.000 Portuguese settled Brazilian countryside by the 17th century. Just remember that most of the Brazilian land was
de jure part of the Spanish Empire because of the Treaty of Tordesillas. Only in 1750 with the Treaty of Madrid the Spanish recognized the Portuguese dominion over that land observing the
uti possidetis principle, recognizing, therefore, the Portuguese colonization of the contested area.
The presence isn't strong just because of a simple reason: Lack of economic value. The Brazilian savanna (the
cerrado) soil just couldn't sustain cash crops as the coastal areas could. (Just like most of Africa). After the exhaustion of the mines, the region entered into a big period of stagnation.
The lack of colonization of Africa before the 19th century has the same simple reason: The land just sucks. The good lands (Zimbabwe, Central African mountais) were just too far from the coast and, even today, most of Africa can't sustain an economical valuable agriculture. So, I think that the economical answer is more plausible then the "biological" one.