Excellent question! The short (and rather unhelpful) answer is that while technically, "a couple" does in fact mean two, it is not always used that way in practice and if you ask several native speakers you're likely to get different responses.
"A couple", "a few", "several"... Words like this are used with various intent. In the particular case of "a couple of weeks" I'm (personally) likely to interpret that as 2-3 weeks away. In any other case where you use "a couple", it depends on the circumstances. I'll get a general idea of what you mean, but we won't necessarily have the same understanding of the situation.
Bob and Marie make a good couple.
Okay, that one's obvious. When you're talking about two people in a relationship as a "couple", clearly there are two of them.
I'll see you in a couple of weeks.
As I said before, this probably means 2, maybe 3 weeks (in my experience). I think this is probably the situation in which you're least likely to cause confusion, though obviously that's not always the case since someone corrected you!
These pretzels are delicious! Can I have a couple more?
Assuming these are snack-sized pretzels... Chances are I'm not just asking you for exactly two, right? Generally people use this to mean "give me some more of them" with "some" being indeterminate. The most common response would be to reach into the bag, grab whatever pretzels you would naturally get at a time, and give them to the person. Sometimes, just to be 'literal' and make a joke, I know people who will carefully count out two pretzels in this situation and give them to you. You'd give them a look, and then they'd give you more. So even native speakers are aware of this disparity, and can find humor in it.
If that's not enough, consider the following xkcd comic, where the author makes fun of the ambiguity of "a couple" and such words:
The author also adds mouseover text to his comic, which reads: "If things are too quiet, try asking a couple of friends whether "a couple" should always mean "two". As with the question of how many spaces should go after a period, it can turn acrimonious surprisingly fast unless all three of them agree." ;)
So there isn't a simple answer for you, I'm afraid, but the answer is it's all very dependent on who you're talking to and how they interpret the word. If your friend corrected you then he has a different interpretation--but that doesn't mean you were wrong!
People understand Ask away by analogy with certain other familiar sentences with away.
Soldiers shout this when dropping bombs from an airplane (see, for example, this book):
Bombs away!
By itself, the word away means "located somewhere else" or "at a distance". In the phrase bombs away!, it suggests movement: "going somewhere else". Bombs away! announces that the bombs have just been released and are now in motion, though many non-soldiers think it's a command to release the bombs. Either way, it refers to the bombs' being "on their way" to their destination, freed from the plane, moving away from the plane, soon to cause damage when they hit their target. A similar sentence is Torpedo away!, said after launching a torpedo (example).
Soldiers say this to mean, "Start shooting your guns, and don't hold back":
Fire away!
Fire here means to shoot a gun. Here, away has the same connotation as in Bombs away!: that you are releasing something that will fly "away" and do damage. It also suggests immediacy and a lack of inhibition. You should eagerly "release" your potential firepower "right away" and hold nothing back.
A metaphorical usage of Fire away! appears in this well-known song from 1980: "Hit me with your best shot—fire away!" The literal meaning is: "Hit me as hard as you can. I am tough enough to withstand it." The speaker is confidently challenging the listener to a fight.
People commonly say Fire away! metaphorically to mean "Ask me all the questions that you want to ask", especially when these questions might be difficult for the speaker to answer, either because they might dig into something embarrassing to the speaker or because the speaker might not know the answer.
When you say:
Ask away!
you are telling your listener to ask any question or questions that the listener wants to ask. The nuance of meaning comes from the way this sentence echoes sentences like those above (and some others, but hopefully that's enough). It suggests that the listener should not hold back or be inhibited about asking these questions, even though the questions might be difficult or upsetting for the speaker.
Ask away! doesn't necessarily suggest that the questions will hit the speaker like bombs or bullets. But this sentence is especially appropriate in situations like a meeting where the speaker must answer hostile questions about something unpleasant or embarrassing, like the "rapid-fire questions" mentioned in this difficult situation. In any sort of context, Ask away! suggests that the speaker is confident that he will be able to address whatever the listener "throws at him". It can also be a way to reassure the listener that the speaker won't take offense to a question.
Notice in the story that the listener, Slughorn, is upset by the question. He suddenly switches from affable confidence to fear. The question appears to hit him pretty hard.
Best Answer
There on would have the basic underlying meaning of onward or forward, as in "they marched on". The sense is the continuation of something.
In your book scenario, the process that is being continued is that when one person finishes reading the book, he passes it on to another person, who reads it (and that process may continue with a third person, and a fourth, etc). The book progresses from one reader to the next.