Australia

Despite the European Union not including all of Europe, a German would definitely call themselves European when describing themselves as a citizen of the EU and not an EUian

Is Australia the entire south of the world?

America is the country's short/familiar name. Like how the Commonwealth of Australia is just called Australia, the United Mexican States is called Mexico, and the Republic of China is called Taiwan.

Mexicans are North Americans

Colombians are South Americans.

Brazilians are South Americans.

Americans are North America but from the country called the United States of America, hence why they get called Americans and Mexicans from Mexico are called Mexicans

Mexicans are americans.

No they aren't.

Colombians are americans.

No they aren't

Brazilians are americans.

No they aren't.

In every country in the anglosphere, the word "America" is synonymous with "United States of America". If you want to speak Spanish and talk about America as a single continent as I know is common in Latin American countries, go ahead. But that is not the way the English language is ever used by native speakers.

It also frankly doesn't make sense. It's based in the popular idea in Latin American countries that there are 6 continents, including one called "America". I know the definition of "continent" is fuzzy and categorising them is ambiguous, but I maintain that the only sensible 6 continent model is one which merges Eurasia, relative to the 7 continent model. If you want to talk about the Americas as a single continent, the only way to do that without blatantly coming across as ridiculous is to have a 4 continent model containing Afro-Eurasia and America.

I'm sure Mexicans, Canadians, Colombians and Brazilians love being called Americans lol

Then why is it the United States of Mexico? Calling them and Canadians just reeks of Manifest Destiny bullshit.