Well I can answer the last question: they want you to kill them sober, so you have a better aim and not waste the bullets.
The different ages for different things in different countries are always arbitrary. There are social and historical reasons that cause this, and in the case of driving even geographical.
The average American kid has access to a car easier, in a vast and relatively empty country with wide and relatively empty roads. And above all, you desperately need the car to get around. The same rules apply in Australia. Europe on the other hand is crowded, with many overpopulated cities, narrow winding roads, and failry reliable public transport. Overall, there is an anti-car policy in the EU and a pro-car policy in the US, which means the last thing we want over here is even more drivers in our already crowded streets.
Similarly, American society condones violence a lot more than sex (and the exact opposite happens on this side of the Atlantic). Your dad will show you how to shoot a rifle at 14, but will freak out if he hears you had sex at 16 (especially if you’re a girl).
And similarly, alcohol (which my grandfather forced down my throat when I was 7) is supposed to be a bad thing in America, whereas Europeans are more lineant towards it. Same goes for smoking, which in Europe is theoretically not allowed for under 18s, but I could buy the cigarettes at any shop when I was 11 and nobody ever asked me for ID.