The image isn't 78 billion light years away. It's maybe....10 (Closer to five? I'm not really sure)...or something close to that number. And yes that is what it looked like 10ish billion years ago.
Farthest away we can (theoretically) see is the age of the universe, some 13.7ish billion light years. Everything beyond that is lost forever to us, never to be seen. It is said to be beyond the farthest
lookback time.
Here's a rather useless link for someone without the necessary physical and astronomical background, but the bit on different distance measures is alright.
http://en.wikipedia.org/wiki/Distanc...28cosmology%29
Any other cosmology/astronomy questions, I'm your guy.