But the most solid argument against the Americans ever crossing back to Old World is that since the Columbus' discovery we had intensive exchange of DISEASES with them, to which neither side had any immunity. They gave us smallpox (syphilis) and clam (gonorrhoea), while we gave them chicken pox and measles. Right at start all these diseases were deadly for those whose ancestors did not leave any immunity for them. Syphilis in medieval Europe acted like a Black Plague, emptying the entire cities - and the fact that it is now a slow-developing disease only shows that most if not each of us had an ancestor who had it. Smallpox was killing American Indians with the same efficiency.
The above shows that the human communities on both sides of Atlantic hardly ever communicated with each other at all - this means that the Africans and Europeans, if in prehistoric times even visiting Atlantis (whoops!) for trade purposes and heard those stories of "outer continent" which Plato mentions, they most likely never were at the continent itself. Even later vikings' visits to Newfoundland were probably short and did not involve contacts with native American population.
"The most ancient native population of Europe which we know is Finnish tribes"
Not only the Finnish tribes, also the Basques. And their ancestors occupied the Atlantic coast of Europe, from Iberia to the UK.
"But the most solid argument against the Americans ever crossing back to Old World is that since the Columbus' discovery we had intensive exchange of DISEASES with them, to which neither side had any immunity"
But that could be explained by the long separation of these populations. If it were true ancient Americans arrived in Europe after/during the last ice age, then they had many thousands of years to build a different immunity against diseases; in short, they became 'Europeans', immune against diseases their ancestors back in America did not develop immunty against.