YES! Yes they are! This is where the history written in the Book of Mormon comes into play (Hear me out before making any judgements)
Indeed, those original inhabitants of northern/southern Americas did come from Asia, but actually Jerusalem. About 600 BC, Lehi, a prophet preaching in Jerusalem, was told by God to take his family, and flee into the wilderness as Jerusalem would be destroyed (ultimately the scattering of the 12 tribes) He and his wife, four sons, and his friend Ishmael and his family, plus another member(Zoram), traveled to a "promised land", where they landed in what I believe is South America. They begin to multiply and populate, shortly afterward finding another group of people that far exceeded their numbers, known as Mulekites. They are remnants of Mulek and some other members, of one of the twelve tribes taken captive. They'd managed to break free and were also guided to this land.
Its recorded about 49-39 BC: "And it came to pass that they did multiply and spread, and did go forth from the land southward to the land northward, and did spread insomuch that they began to cover the face of the whole earth, from the sea south to the sea north, from the sea west to the sea east.". I did calculations once on the population of people (JUST Lehi and those that came with him) if they doubled every generation from 600 BC to about this time frame, we have 6,710,886,400 people. EASILY could cover both continents.
The difference in languages is mostly from conquests/raids/other nations claiming the land. Mexico and below is mostly Spanish and some Portuguese, due to Cortez/Christopher and other such people from Spain/Europe. Canada is mostly France and England, the US England...
Now, people might argue Native American decent doesn't come from Jews, which may be true, but does not disclaim that they came from Israel: "It has become customary to use the word Jew to refer to all the descendants of Jacob, but this is a mistake. It would be limited to those of the kingdom of Judah or, more especially today, those of the tribe of Judah and his associates. Thus all Jews are Israelites, but not all Israelites are Jews, because there are descendants of the other tribes of Israel also upon the earth" Lehi is a descendant of Manasseh, and so his family would be also. The tribes of Zoram, Ishmael and his family, as well as the Mulekites, are not known (or at least not any that I recall)