There is no clear definition of what steampunk is. I don't know where you're getting the whole 'functionality' thing from, but steampunk is still a genre that is defined a lot by personal interpretation, usually with only two common aspects- that it is based off of the Victorian era, and in the case of steampunk stories, steam became the major power source of that era rather than petroleum.
This is honestly one of the reasons I try not to interact with the steampunk fandom. There is always that one person who thinks that they know EXACTLY what steampunk is, and if someone else disagrees, well, they're obviously not steampunk! Clearly, you've never been to a steampunk convention. There are tons of costumes with parts that aren't 'functional'. Doesn't mean they're not steampunk though.
Don't know. But plenty of steampunk cosplayers do it. My point was that there is no clear definition of what steampunk is, so just because they do add pointless gears to hats doesn't mean it's not necessarily steampunk.
It's historical fantasy but that said there are still rules to it, guidelines and ideals that must be followed because otherwise you're just playing dress-up with some junk you found at a scrap yard.
They don't teach steampunk in school for the same reason they don't teach cyberpunk or LARP (except for Drama Club but that's entirely different). Because it's something you do in your free time and just like any fandom there are people who are going to completely miss the point and fuck things up just by being part of it.