In the Netherlands we use the "US International" keyboard, which is basically qwerty like you're used to but with dead keys to make áéàüetc. We don't have that many odd characters so it's okay not to have special keys for it, but I'd agree with anyone saying that even these few are too many. If we're gonna clean the language up though, let's also get rid of other overhead. For example the sentence "If we clean language though, rid other overhead" makes quite a lot of sense.

Other countries that make even less sense and use way too many special characters (from my blunt perspective) usually have different keyboards. Prime example that I know of is France where you have to use the shift key to make numbers.

To answer what you actually asked: Yes we are taught how to make those special characters. For me it's as logic as typing parenthesis or the euro sign, but I'm spending most of my waking hours typing one thing or another. Many people don't or barely know how to.

It's not what most of the time is spent on in those courses. We're being taught the asdfjkl; row just like everyone else. Or aoeuhtns, depending on your keyboard (in the Netherlands we only have qwerty though). Making accents is more of a side thing that's mentioned once or twice after learning everything else at an acceptable speed.