I would be interested to know whether in the USA or other countries, exist similar projects such as virtual nations, fictional nations or micronations.

In Germany exist ca. 30-50 virtual nations with about 100-200 players.
Typical characteristics of german MNs are a forum/board like this, a claim on a MN-worldmap and interaction in politics, culture, sports and other parts of a real society. On average there are 5-10 players on a MN, sometimes more, sometimes less.

I know, that there are virtual-nation-projects in poland, france, GB and even brasil. But I wonder, that this kind of simulation is not present in the USA.

I would be lucky to get know similar in the whole world.
If you are interested in the german mn-subculture, I could give more infos.