Cosmic Microwave Background seen from a hypothetical foreign Galaxy? My basic understanding of the CMB tells me that this 'wall of radiation' is currently the furthest electromagnetic wave from our position that we can detect. Through relativity we know that objects far away are seen in an 'older' state due to the emitted photons taking time to reach our measuring tools.
My understanding is that as there is effectively no centre of the universe, so the CMB was emitted from every point of the universe roughly 300 thousand years after the Big Bang as it cooled and expanded. I understand that the CMB we detect today has travelled roughly 47 billion light years to reach us (EDIT: unsure on figures) and therefore we are effectively seeing the universe roughly 13.8 billion years ago.
My questions are as follows. Suppose we are an observer in a hypothetical Galaxy X located 47 billion light years (EDIT: unsure on figures) from the Milky Way Galaxy. We launch our own microwave detecting satellite and survey our sky. 
If there is no centre or starting point of the universe, when we look out far enough from Galaxy X do we see the same CMB beginnings that an observer in the Milky Way Galaxy sees?
When looking back towards the Milky Way Galaxy do we simply see CMB from roughly 13.8 billion years ago?
If everywhere is effectively the centre of the universe, I would expect an observer from every Galaxy in the universe to see the same CMB? 
If there was an observer at every point of the universe, would we expect them to all see the same CMB when looking out with microwave measuring equipment?
Would they all argue that they are in the present time and every direction they observe at far enough distances are further back in time?
Am I on the 'right track' here?
Cheers,
Dan.
EDIT: unsure on figures.
Questions still stand to be answered.
 A: The CMB will look very nearly the same to both us and your observer on a distant galaxy.
Your argument is correct. Our model for the expansion of the universe is based on the assumption that the universe is the same everywhere - technically that is it isotropic and homogeneous. Though at the current time this is obviously untrue on the small scale (because we have dense objects like stars separated by vacuum) it appears to be true if we average the matter distribution on a large scale. And at the time the CMB was emitted, well before any stars formed, the distribution of matter was homogeneous to better than one part in $10^5$.
So we expect that for every observer everywhere in the inverse the CMB is going to look the same - to about one part in $10^5$. That one part in $10^5$ is the fluctuations in the CMB most recently measured by the WMAP experiment. The current favourite explanation for these is that they originated in quantum fluctuations during cosmological inflation, and because these fluctuations are random they are randomly distributed and will look different for different observers.
However, even the fluctuations will look the same in some respects. Though the detail of the fluctuations will be different for different observers we expect that their power spectrum will be the same for everyone.
A: In fact, the CMB could look substantially different.
The strongest feature on the CMB is not its well-known speckle pattern, but a blue/redshift dipole due to the movement of our local group. This dipole is usually removed in most representations.
In a very distant galaxy, this dipole could be absent or stronger or point in another direction.
