Yes. If the photons have travelled 10 billion years, that means you are seeing the galaxy as it was 10 billion years ago.
13 billion light years (rounded)
The distant universe is seen as it was when the light we see now left it, this is as much as 13 to 15 billion years ago.
The most distant stars we can see (at least in principle) now are almost as old as the Universe; so, about 13 billion years.
It is not currently known how big the Universe is. The observable Universe has a radius of about 47 billion light-years; that is, the most distant objects that can be observed in theory are at that distance. The actual Universe is probably quite a bit bigger.
Astronomers have found a mind-bogglingly large structure so big it takes light 10 billion years to traverse in a distant part of the universe.
If you look at a distant galaxy, the light from the galaxy has travelled for perhaps a hundred million years, a billion years, or up to an age close to the age of the Universe (13 billion years or so), depending on the galaxy's distance. Thus, the light you see shows you how the Universe was billions of years ago.
The most distant known source in the universe is a galaxy called GN-z11, which is approximately 13.4 billion light-years away from Earth. This means that the light we see from GN-z11 today started its journey towards us over 13 billion years ago.
Far or near, all galaxies were thought to be formed in the first half billion years of the formation of the universe ... that is, about 13 billion years ago. Note that we're seeing the distant ones in a younger stage of development.
explorers
Astronomers have spotted the most distant object yet confirmed in the universe - a self-destructing star that exploded 13.1 billion light years from Earth. It detonated just 630 million years after the big bang, around the end of the cosmic "dark ages", when the first stars and galaxies were lighting up space.
No. At that distance, the Universe is essentially "flat". If there is a curvature - this is not confirmed - it is at a much larger scale, at distances which we can not observe.
Pope Benedict XVI usually traveled by chartered airliner, AtItalia, when he traveled to a distant country.