Alright, I will give the answers to 2 and 3.
2. The Chinese are theorized to have discovered the Americas (and a large part of the world) in a huge national undertaking to explore and map the world around 1421, which is well before Columbus. There is quite a bit of physical evidence to support this claim, which has been culminated in the book 1421: The Year China Discovered the World. Here are some links:BBC Article http://www.1421.tv/the_book.asp
The theory doesn't have popular support, but what new theory does?
3. Neo-conservatism got its most prominent start amongst 1960's ultra-left wingers who denounced popular post-Vietnam anti-war sentiment. Most liberals in this era considered international intervention an incredibly bad idea based on the fallout of Vietnam (traditional republicans supported this ideology as well), but neo-cons considered democracy an inherent right to all of those in the world and should be spread, by force if necessary. NeoCons consisted of a small sect of collegiate level students and professors who disagreed with their liberal brethren. Once Reagan came to power, these ultra-left wingers sided with the Reagan administration who proposed an imaginative, non-practical approach to spreading democracy throughout the world. Neocons have been considered Republicans since then.
I brought this up because it is probably one of the most ironic pieces of American history I have come across.