The CMB origin at about 380,000 years after the Big Bang is indeed the furthest we can see, IN THE ELECTROMAGNETIC spectral domain. And you are right that this is not about the full universe vs the observable universe, you are talking about a portion of the observable universe which is simply occluded from us not in principle, but because photons could not propagate from freely out until then.
So, theoretically the universe is about 13.8 billion years old, and we can 'see' into the past only to 380,000 years after the Big Bang.
The reason we don't stop there, in either theory or in understanding what's behind that apparent 'wall', is that 1) we know a lot about what happened before the 380,000 year 'wall' from what needed to be there in order for us to see what we see after, AND maybe more important
2) for those who don't believe what they can't see, we will be able to see behind the 'wall' with gravitational waves.
Gravitational waves (GWs) are affected little by that 'wall' and all we need to do is build a large enough interferometer pair, to see them. LIGO which detected GWs from black holes merging, cannot detect those cosmologically originated GWs because their wavelengths are much larger. We need space based interferometers with legs a million Kms or larger -- that's in the planning for the next decade, with 2 or 3 satellites forming the 1 or 3 legs (funding dependent). And later bigger ones. We spect to see behind the wall using that gravitational astronomy.
As for your 3 questions:
Matter behinds the wall. We know there had to be matter, but it was mostly uncondensed and very energetic charged particles, mostly electrons and protons. At 380,000 years they recombined into hydrogen atoms and a few other things, and the photons we see now as the CMB could escape. We know actually a lot more, eg, about the very small inhomogeneities and anisotropies in the CMB which came from the same on the density of matter, and which served as seeds of galaxies and stars. Before electrons and protons it was even hotter, and it was quarks, gluons and electrons and a few other particles, and before that particles we have not seen in the lab. We know the basic physics for those things but still expect there will be more energetic particles, perhaps remnants of the Big Bang that became dark matter, and other exotic particles. As it gets hotter it's quantum gravity like string theory claims, and for which we still don't know what the right theory is.
We do think we know that there are galaxies that we can not see now. Even many of the ones we see now, emitted their light long ago, and will not see their light emittEd now ever. They are traveling away from us now too fast, and light emitted from them will never reach us. But we are seeing the light from many such galaxies now, that they emitted billions of years ago. Yes, the cosmological horizon is, we think, real
Nothing overtook the CMB. Galaxies and stars were formed maybe a few million years after tHe CMB broke free. Remember the universe was expanding, so if they are younger than the CMB they were created closer to us, and it's why we can see them. General Relativistic geometry can be tricky, but for cosmology it's good to think in terms of time from the Big Bang or back from us. Keep in mind the CMB was released everywhere in space, and what we see now are photons that reached us now. They traveled for 13.8 billion minus 380,000 years. We have seen galaxies going back to a couple hundred million years from the Big Bang (but sorry, I may not have the number exactly right, or most updated).
For an intro to the chronology of the universe see the wiki article at
https://en.m.wikipedia.org/wiki/Chronology_of_the_universe
It's got the different cosmological periods or epochs, including the recombination time (the 'wall') and other important cosmological times. We still have a lot to learn, but the most mysterious epochs from our knowledge of elementary particle physics are those that are the earliest: the Planck epoch (we just don't know what makes thing up then, maybe string theory or other quantum gravity theory will get to it sometime), the strong unification era (we know a little bit after how and when the stron and electroweak force unify, but still plenty uncertainty), and the inflationary epoch (we have inflation theories, some version seems right but we're not sure which, or the field that caused it). We tend to know a lot about the rest, from theory and observation, but still we think we'll find surprises.
Your final two questions:
A. The current observable universe is about 46 billion light years in radius. We see pretty far out, but have not seen the edge, or what is called the horizon (we would not fall off). Unfortunately, if anybody is around in a quite few billions of years we will see even the closest galaxies get too far from us to be able to see them (or their successors) because the expansion will have taken them past our then horizon
B. There will always be CMB around as they were created everywhere in space. However, they will be way way redshifted- right now they've been redshifted by a factor of 1100, and we see it as high microwaves, 100 Ghz range. Another factor of a million say they'll be 100 KHz but much weaker, and eventually they'll get too weak and low frequency for us to detect.
