Good question! And lamentably, one which certainly cannot be suitably answered by a post or two on a message board. While I don't pretend to be an authority on the subject, I would refer you to "Kingship at its Source" by Dr. John Davis Pilkey, which deals with your question head-on.

Ultimately, regarding the dates, reconciliation between secular chronology and biblical chronology can only take one of four forms. Either the secular timeline is pure bunk (a view to which no one I know holds), or the biblical timeline is pure bunk (non-believers tend to embrace this one), or the biblical timeline is truncated, likely via genealogical gaps (this view is held by a lot of liberal Christians), or the secular timeline is protracted (this view is held by most conservative Christians). I'm inclined toward the view that the secular timeline is protracted, but as far as arguing the finer points, I'm perfectly content to concern myself with matters of theology and leave these sorts of matters to experts like Dr. Pilkey (who, I believe, holds the same view that I do).

As far as population growth is concerned, I'm not entirely sure I understand your question. Would you mind elaborating on it?

As for the migration to America, this is fairly easily accounted for. Prior to the flood, there was but one m***ive continent. During the global catastrophe, such damage was dealt to the earth's surface that the land m*** split into several continents. Those continents began to visibly separate and drift away from one another in the years following the flood (see Gen. 10:25. In the days of Peleg, "the earth was divided"). There would've been ample time for some descendants of Noah to settle in the land-m*** that would in time become the American continents.

Hopefully that all made some sort of sense, and was at least somewhat helpful.