1) Yes, the universe is 14 billion years old.
2) When we see the farthest possible objects, the light has been traveling for 14 billion years (or nearly so). When the light left the object, it was a lot closer than 14 billion light years away. At the present time, however, the object is roughly 40 billion light years away.
3) Since we can see objects in all directions that are currently 40 billion light years away, we can say (in a certain sense) that the observable universe is 80 billion light years. (Some may give slightly different figures, such as 94, but let's not argue about that.)
4) The inflation phase of the universe lasted an extremely short time, but the expansion of the universe has occurred continuously (and, in fact, is accelerating) over the life the universe.
5) Finally, this volume of diameter 80 billion light years is an indication of the *current* size of what we can see. There might be much more to the universe than that, so you should really qualify this number as saying that it's the diameter of the observable universe, and not the whole shebang.