Can the age of the universe be much bigger than 13.8 billion If observable universe is only a small fraction of the existing universe, does it imply that the age of the universe is much more than 13.8 billion years or the expansion of the universe is much faster than what we know ?
 A: Although there is some current tension about the expansion rate, it is measured quite accurately, and the age of our observable universe is derived from that (and other observables). What you mean by the 'age of the universe' (so explicitly NOT only the observable universe) can be different depending on your model. If you just look at the standard Big-Bang model and assume that the universe is as homogeneous and isotropic, which is usually done, than the time since the Big Bang happened is the same even outside of the observable universe, no matter how large it is (the current observations leave it open if the whole universe is just much larger than the observable universe, or infinite).
If you also consider the theory of cosmic inflation (proposed to solve some problems with the Big Bang model and capable of explaining the inhomogeneities we observe from initial quantum fluctuations that have been exponentially enlarged) the situation could be different. Note that inflation in general is now considered part of 'standard cosmology'. In inflation, what we observe as Big Bang (i.e. the very hot thermal bath of all the particles we know expanding non-exponentially) was the end of inflation giving rise to all the known particles in a process called 'reheating'.
Inflation needed to endure for some time to solve some of the cosmological problems. The duration of inflation is usually not given in any time unit, but in $e$-folds, the time that is needed so the universe grows by a factor of $e$. Different models usually predict the number of $e$-folds needed to solve most of the cosmological problems inflation is supposed to solve, but it can very well be that it lasted much longer.
In 'eternal inflation' models, inflation still goes on in most of the universe, and in only a small fraction (if I am not mistaken a measure zero fraction) of the actual universe inflation ends, while every such 'pocket' calls their end of inflation 'Big Bang', and measures time from that point on, while in other parts of the whole universe, inflation goes on, and in other parts, the respective Big Bang was earlier. If I am correctly informed, eternal inflation models are seen with skepticism by a lot of cosmologists, as are a lot of proposals concerned with things outside the observable universe. Also note that Alan Guth et al showed that inflationary space-times are not 'past complete', i.e. that inflation cannot be the initial state of the universe, i.e. cannot have gone on 'forever'. I am not sure if this has been disproven since then.
A: Every black hole is basically an "edge" of our Universe. Or at least of our observable Universe.
I don't think that notions of how "big" something is, (in this case the Universe) has any meaning withought speaking of the observer. Who is observing? Because from the perspective of someone with constant acceleration towards the speed of light, the Universe is approaching zero length. So it could be, that the Universe is equally infinite as it is infinitesimal, all depending on the observer.
If you are asking how far you can go before hitting some edge (other than a black hole) (I could be wrong but) I think that there is nothing in our intuition or our physics that seems to indicate that there is an edge anywhere in the Universe. The only indicator would be if we were to find that spacetime of our Universe isn't flat (so far we know that it is), at least that would indicate that there is some "edge" that you can only reach if you could detach yourself from space and time.
But either way we can't, so as far as we are concerned there is no edge in our Universe. At least as far as I know :P
