Hi Greg

your first question is quite difficult. Stars always occur inside of galaxies, and so the most distant star that we can see must be in the most distant galaxy we can see - although the individual stars in a galaxy cannot be separated out, so they don't have their own names. Only stars that are pretty close to us, inside our own galaxy, have their own names.

The most distant galaxy we can see is 13 billion light years away, but not even it has a name yet! There is too much in the Universe to give it all names. You can read about it here http://www.msnbc.msn.com/id/4274187/

There is one very distant star (of sorts) that we gave a name to. It is called
GRB 050904 and it is also 13 billion light years away. It is not a regular kind of star like the Sun though, but a rapidly spinning stellar 'left-over' - something left after a massive star dies - with an extremely strong magnetic field. It is a type of star called a magnetar.

NASA can see back pretty much right to the beginning of the Universe, about 13.7 billion years ago (actually, we can only directly see what was going on about 3 minutes afterwards). The radiation produced at that time is known as the Cosmic
Microwave Background Radiation, and it has been observed by several satellites, including NASA's WMAP satellite

keep asking those difficult questions!
Lyndsay