Quite a lot is up for debate about exactly how early galaxies formed, but there is no debate about the fact that stars are still forming within galaxies.

The "original" stars that formed are mostly designated "Population II". Population II stars tend to be older, and to contain a much smaller percentage of heavy elements than Population I. Often found in galactic nuclei and globular clusters.

Population I stars are younger, and usually richer in heavy elements. The consensus is that they formed from the debris left over from nova and supernova explosions of Population II stars, which would have, by the time they went nova, have fused a fair percentage of their original hydrogen content into heavier elements.

They're still being formed now...we can observe this in certain nebulae. They tend to be found in the spiral arms or outer areas of galaxies, and it's likely that they're the only stars that would be able to support the formation of rocky planets.