Well. My best shot at the most distant, individual stars we can see is discussed in the answer to Question 614. The Hubble Space telescope is routinely imaging individual Cepheid Stars in galaxies out to the Virgo Cluster of galaxies. There have also been supernova seen out to distances well over 500 million light years; these are individual stars that have exploded so we can resolve them as individuals even though we cannot see anyother stars in their host galaxies.
As for galaxies, this record changes every few months, but in the answer to Question 1253 which was about the youngest galaxy discovered, and Question 927 about the most distant objects known in the universe.