The first stars to form in the universe may have had very different properties from later generation of stars. They were uniquely made form just primordial gas and also their formation process and characteristic masses may have been quite different. No direct observations of these star are possible at this time, however, so our ability to study these early stars is limited to indirect measurements and numerical simulations. For example, stellar forensics based on nucleosynthesis patterns preserved in subsequent generations of stars may be used in an attempt to reconstruct the properties of the first stars.
The overarching big questions are: What are the typical masses of this first generation of stars? What is the initial mass function? And how did these stars live and die? This will determine how the universe transitioned from the first stars to the formation of the first galaxies, and what observations of them may be possible in the future.
Early simulation of formation of the first stars and simple theoretical arguments suggested the these first stars may have been quite massive, possibly massive enough to explode as pair instability supernova. Interestingly, there is an increasing number of observations suggesting that even in the present universe very massive stars form and live to explode as powerful pair instability supernovae. But is this also outcome we should generally expect for the majority of the first stars and is it supported by observations of the "ashes" of the first stars?