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!
Best Answer
"That's that" can generally mean "that's all" or "that's the end", or even "that's it", in the sense of "that's how easy it is".
If someone asks you how to make a cake, you might give them all the instructions and then say "that's that!", as in that's all, that's the end of the process, and that's how simple it is.
Of course, it can also mark the end of a discussion because of the "that's the end" meaning: "No you can't go to the party, and that's that!" Looking at the previous question, "Today's lesson will only cover the introduction about the course. And that's that" seems to have more of this kind of tone, so it would be better there to say "that's all" or "that's it". But of course it also depends on how it is spoken: with a big smile, "And that's that" would seem perfectly appropriate, whereas it seems harsher in writing.