If so, why didn't human evolve into different species at earlier time (not too far back from now) when the interconnection was not good?
We did evolve into different species earlier --
Homo erectus, Neandertals (which were on the fuzzy edge of being a different species),
Homo floriensis (probably), and others even earlier.
If you count the time scale, we should have seen significant evolutional change already.
In ~500,000 years of separation, Neandertals and the African ancestors of modern humans became noticeably different, but not so different that they couldn't interbreed. You're talking about one-tenth that time. Why do you think we should have split into different species in 2000 generations?
How long have Eskimos existed? Are they becoming a different human species?
Perhaps 8000 years. Genetically, they're about 50% derived from a relatively recent (<10,000 years, probably) migration from Asia, and 50% from the earlier migration represented by other Native Americans. They have not existed as a separate group for long, and they've had substantial interbreeding with surrounding populations throughout; even quite modest amounts of gene flow usually prevent speciation. So no, they're not becoming a different species. They are a reasonably distinct population, probably with their own set of local adaptations.
Is their genetic code much more different from ours then the difference between, say, whites and blacks?
I don't know who you mean by "ours" here -- is there some default ethnic group for CF readers? They are genetically more similar to east Asians than Asians are to Europeans or Africans, and more similar to Europeans than Europeans are to Africans.
(Note: you don't mean different genetic codes. The genetic code is the mapping from DNA to amino acid, and that is identical for all humans. You're just talking about genetic difference.)
Is there a list which compared the genetic codes among different races?
There are extensive data sets of genetic variation within and between many populations. Eskimos, in particular, were studied in a paper that came out last month.
Inter-racial marriage is still rare compared with the general population. Are we seeing that the genetic codes of African people departing away from that of Asian people?
Intermarriage (and more relevantly, interbreeding) is extremely common, genetically speaking. What differences there are between populations were largely the result of isolation by distance, and that has disappeared with modern migrations and transport. Difference are being homogenized much faster than they are appearing.