cosmology - What is the best evidence/theory about the first generation of stars

In particular, during what range of years after the Big Bang did the stars form? What is the expected range of masses of these stars and what is the expected lifetime before they supernova? I assume these stars resulted in the re-ionization of ISM (interstellar medium), so what is the evidence and estimates of the age of the re-ionization era?

Answer

I'll take a swing at this, but bear in mind that you probably won't get definitive answers because you're asking about two active and difficult areas of research (pop III star formation and re-ionization). I'll answer the particular questions, but I'm hoping you get a feel for the fact that we don't have clear-cut answers yet.

During what range of years after the Big Bang did the stars form?

The consensus is somewhere in the range $20

What is the expected range of masses of these stars...

This is really, really hard to answer. Until about a year ago, consensus was settled on a very heavy mass distribution, with many (if not most?) stars in a range 100-1000 $M_\odot$ (see e.g. the 2004 review by Bromm & Larson). This is argued on the grounds that the smallest gravitationally unstable mass in a homogeneous isothermal gas, the Jeans mass, runs like $T^{3/2}$ and primordial gas cannot cool as much as metal-polluted gas. The difference in temperature is about a factor of 30, so pop-III stars would naively be about 100 times heavier than modern stars, whose mass distribution seems to peak around 0.5 $M_\odot$.

However, recently (as in, articles in Science in the last few weeks) have reported very detailed simulations of early star formation where the stars stop their own growth as they start to radiate. The result is stars that are a few times 10 $M_\odot$. Still very big by modern standards, but not as big as previously thought. So the jury is out, IMO.

... and what is the expected lifetime before they supernova?

Well, it depends on how large they are, but broadly stars of about 40 solar masses last about a million years or less. How they evolve is unclear because it's difficult to compute the rate at which they might lose mass from their surfaces.

I assume these stars resulted in the re-ionization of ISM (interstellar medium), so what is the evidence and estimates of the age of the re-ionization era?

The role of pop III stars in reionization isn't at all clear. This is slightly outside of my own work, but from my own knowledge I think it's quite well known that ionization was complete by about redshift $z\approx6$, which is about a billion years after the Big Bang. Remember that many pop III stars could have already been born, evolved, and died, producing enough metals to produce pop II stars in the next generation. Working out just how much radiation had been poured out is theoretically very difficult.

However, as far as I know, observations of a $z=7.085$ quasar have given us some idea that the intergalactic medium around it wasn't re-ionized. So its more likely that stars after pop III (and maybe AGN/quasars?) had more to do with re-ionization because it happened broadly later than they were born. That's just wild speculation on my part, though.