Universe is expanding at enormous speed
I'd like to expand a bit on the answer to the second question, but for completeness I'll do both.
As said in JasonR's answer, the expansion of space isn't limit by the speed of light. So objects can be moving at moderate speeds, but because the space between them and us expands faster than light, it's emissions will never reach us. For this reason, there are already regions of space that are beyond our horizon. Whether or not this will always be depends on what "Big Thing" your cosmology ends with. If it's a "Crunch", then everything comes back together in a reverse "Bang" at the end of time. If it's just a "Freeze", then the acceleration expands and possibly even accelerates forever.
Abraham Loeb wrote a curious paper (available on the arXiv) about how to reach cosmological conclusions in the absence of nearby galaxies. About 100 billion years from now, all the galaxies in our Local Group will be beyond the horizon of the Milky Way (or rather Milkomeda, after the Milky Way collides with Andromeda), and the CMB will be at a wavelength longer than the observable Universe. But you'll still be able to reach conclusions about cosmology by using hypervelocity stars being ejected from the galaxy. The point is that you can still get accurate results about the global structure of the Universe using local results.
As for our current model, we have a great deal of evidence that the cosmos is structured according to the Concordance Model. You can always say "it might turn out to be wrong", but it can't turn out to be that wrong because of said evidence. It's like GR as a generalization of Newtonian gravity: yes, Newton was "incorrect" but his theory was also quite accurate, to the extent that we still use it for, say, N-body simulations of star clusters.
The expansion of space itself is not limited by the velocity of light. Even now there are parts of the universe that are receeding from us at a relative velocity greater than that of light (hence why we have observable vs. actual universe terminology).
We're not really sure what sort of conclusions any far future scientists will draw at such a distant time. Perhaps the CMB will still give them the clues they need to figure out that the galaxy itself is not the entire universe? However, it is always possible that we have something totally wrong. That's the beauty of science, they follow the evidence. And just because they figure out that something they thought was right is actually wrong, is no excuse to substitute whatever harebrained idea in place of what the evidence supports (religions, mystics, Deepak Chopra, etc. are notorious for that sort of BS).