Skakespeare made use of sarcasm. So no, Hollywood did not invent it.

In the UK, yes, definitely.

It's also popular in Asia. Seems it's exist everywhere

Sarcasm is a human characteristic, some people are likely to be ironic more frequently than others, though it is a great way to use humor, mainly in talk shows, movies and comedies in general. As you get used to the context (historical, social, cultural) of the language you're learning, it becomes easier to get the point of a joke.

Interesting question. Sarcasm isn't just an American thing. It's certainly used in British culture, mainly as an easy way of momentarily getting the upper hand or earning a cheap laugh. It's also used in other European languages.