1., however, is all wrong. In the coordinates you are using, space is expanding, and that means that, while the CMB emitted from some distant point is moving towards you at ##c## measured locally, it does not get one light year per year closer to you. The universe has expanded by a factor of about 1000 since the CMB was emitted, so the point in space that emitted the CMB radiation we are just seeing now was 1000 times closer to us when the CMB was emitted. The approximate figures, IIRC, are 42 million light years away when the CMB was emitted, and 42 billion light years away now. The CMB was emitted about 13.7 billion years ago (about 300,000 years after the Big Bang, but that time is rounding error compared to the total age), so even though the point of emission of the CMB radiation we are seeing now was only 42 million light years away when the radiation was emitted, it still took that radiation 13.7 billion years to reach us.