All good questions! The more we learn, the more we know we don't understand.
Certainly if this quasar is at 13 billion years, then we are looking back 13 billion years. This object may not exist anymore - in fact many stars beyond a few billion light year would presumably be reaching the end of their lives or beyond the lifetime. Objects out at 10-13 billion years, may no longer exist, but we will not know because that light won't fade for billions of years. Anyway . . .
Active galaxies are galaxies which have a small core of emission embedded in an otherwise typical galaxy. This core may be highly variable and very bright compared to the rest of the galaxy. Models of active galaxies concentrate on the possibility of a supermassive black hole which lies at the center of the galaxy. The dense central galaxy provides material which accretes onto the black hole releasing a large amount of gravitational energy. Part of the energy in this hot plasma is emitted as x-rays and gamma-rays.
For "normal" galaxies, we can think of the total energy they emit as the sum of the emission from each of the stars found in the galaxy. For the "active" galaxies, this is not true. There is a great deal more emitted energy than there should be... and this excess energy is found in the infrared, radio, UV, and X-ray regions of the electromagnetic spectrum. The energy emitted by an active galaxy (or AGN) is anything but "normal". So what is happening in these galaxies to produce such an energetic output?
There are several types of active galaxies: Seyferts, quasars, and blazars. Most scientists believe that, even though these types look very different to us, they are really all the same thing viewed from different directions! Quasars are active galaxies which are all very, very, very far away from us. Some of the quasars we have seen so far are 12 billion light-years away! . . . .
http://imagine.gsfc.nasa.gov/docs/science/know_l1/active_galaxies.html