I was under the impression that the science guy put in the request for his team before leaving, but then again, I don't know how long they've been there. There have been 10 pilgrimages, and they have been in Terra Nova for 10 years, so that's 1 a year if that's the logic. If they only do one a year, and the doctor put in his request before leaving, it would make sense that her departure was delayed due to other getting in first.
As for the unknown species, that could be chalked up to one of two things; 1. their bones didn't survive the eons that passed between them and humanity or 2. they only exist in the separate time stream.
With the beacon and sending people through, they could very well just be guessing. The future is overcrowed and polluted, so if they can send thousands of people of away with a premise of a better future, so be it, even if in reality it means their deaths.
As for the doctor knowing about the jail time, again, that happened over the course of years. I forget now how long they said he was in jail, but it was a few years.
They have some means of steady communication, and judging by the distances they can communicate over, I would say that it is a satellite.
With the family, no they did not arrive 180 apart, rather during the first transfer they didn't realize there would be any delay, or they weren't using enough power, but then that would beg the question why change procedure if they didn't know anything was wrong?
What bothers me is that one of those bird things flew into the weather balloon. I don't think they fly satellite high, but they definitely fly higher than birds.