"Also, I've read much speculation that the Mandans may be the remnants of the Prince Madoc (Welsh) group that came to the US in 1170AD...Lately I've read 540AD."
I think that story belongs in "Chariots of the Gods" or Atlantis.
A number of recent books have theorized that the Americas may have been settled in remote times - post glacial - by separate waves of settlers from Asia, possibly western Europe and even Africa who melded to produce the modern Amerindian, but the last waves of immigration from eastern Asian Mongolian Type people predominated. Contemporary Amerindian Languages fall into three groups: the mainstream Amerindian languages, Athabaskan languages and the Eskimo-Innuit Languages - in order of probable arrival from Asia. Some linguists believe that more than 11,000 years was necessary for the degree of diversity noted in the non-Athabaskan, non-Eskimo type languages to have developed.
They also note that the number of different Ameridian linguistic families increases as you go from east to west across the North American continent which tends to indicate that the original dipersal point was somewhere along the west coast of North America.
There have been other studies done on blood types linking Amerindians predominantly to eastern Asians with one possible blood type found in western Europe - and NOT derived from recent intermarriage.
I read a recent book about a theory that eastern Asians, possibly linked to the Ainu type people, sailed around the north Pacific during Glacial times and actually made it further south prior to the glacial retreats beginning around 11,000 B.C. There was an ongoing argument for some time between the pre-Clovis and Clovis theorists, but there have been pretty convincing finds in South America and eastern U.S. to indicate that there were modern human types in the Americas well before the Clovis culture.
As for historic visits prior to Columbus, I haven't read anything serious other than indications that Norsemen were clearly here in the 1000's. probably from Greenland and definitely in Newfoundland where a Norse settlement has been actually unearthed.
Hey, we have a plaque here at the mouth of Mobile Bay (Ft Morgan) commerating Prince Madoc's landing here in 1170AD. (No kidding)