Thanks, guys, I see all of your points.

First, I lived in Australia for a while, and I think I carry a lot of its accent. So I tend to agree with Saikat.

What Phil said, about the European languages having similar intonations in general, is basically what I feel. It's like when a book is teaching the difference of R and L. Okay, it's important for those who speak languages that don't have this sounds, but... Well, it's redundant when our own language already have this sounds.

My point, however, was answered by Susan. So, native speakers do this so naturally that they don't realize, and when they listen to something different than this, they know something is wrong, but not exactly what. Right?

I still don't like this subject (sorry), but you all gave me a different perspective. As a matter of fact, what Alan pointed out, the intonation before comas, is the topic for a next class I'll be giving, and I was unsure on how to approach it. I loved the video Peachey sent, but I think I might use one from an Australian comediant, who exagerates it a lot, so it's easier to see how this really makes a difference. (https://www.youtube.com/watch?v=KpBYnL5fAXE)

Thanks so much, guys, and I sure will come back to ask for help with future classes. :P

I teach intonation from elementary level upward, and the students manage it perfectly well (the intonation for the questions you mentioned were part of an elementary lesson I taught about two months ago). When they get it right, they do sound natural.

Yes, it sounds funny because it sounds unfamiliar and sing-song, so why not teach it as something fun?  Even more, I'm pretty sure your students want to sound as natural as possible, so they wouldn't mind training that way.

For your amusement, this is a case of when intonation doesn't go as expected... :D

https://www.youtube.com/watch?v=5wB0OkcCps8

While it's true that "intonation" is much more complex than simply "rising/falling", we can just teach the basics to learners. I think at the very least teaching rising intonation for questions vs. falling intonation for statements makes the learner sound much more natural.

Also, as Phil pointed out, it matters in listening comprehension too. If the learner can hear the rising intonation at the end of a sentence, they can at least guess "Ah, they're probably asking me a Y/N question!", which makes it much easier to contextualise the speech.

Slightly more advanced (but still very teachable) is rising intonation before commas, which leads me to your third example. I don't think it's related to questions, but rather to lists. Whenever we list things we use rising intonation for all the items except the last. The red syllables = rising and the black = falling.

I need a can of cola, a bag of chips, a box of chocolates and a packet of gum.

My number's one-five-two, three-two-three-three, four-four-six-seven.