Well The [i]Unity[/i] was the only colony ship, the seven factions were created out of the original colonists, the leaders themselves avid users of the Longevity regimen. You are correct that, at the time of the RP, the humans have been on planet for a couple hundred years, enough time for several generations of "Planet born" humans to pass, and for the factions to build into the nations. It should be noted that there has been [u]no[/u] contact with Earth at any point during this time, not during the 40 year Cryo Sleep journy to Alpha Centauri and not in the 350 years after, and due to the state of the Earth when the [i]Unity[/i] left it is widely thought that the old nations of Earth have long since destroyed each-other, as well as all human life on Earth. 

Now, Normal Probe Teams are basically spies and special operatives used by the various factions to steal resources, tech, sabotage buildings, assassinate researchers, etc. The role of this Probe Team however is flipped so they are more or less a Hunter team designed to eliminate certain rouge individuals and organizations that have been deemed to be a threat to all factions (things such as small terrorist cells, researchers that have gone rouge and have begun developing Bio weapons and so on), but instead of working for one Faction the work for the entire Planetary Council (a council made up of all the leaders of the factions, think of it like the UN but much smaller). It might be easier to explain the team along the lines of Specters from Mass Effect, only with a more Hunter Killer slant. Also the team is made up of members for all the different factions, and not just one.