In Spanish, América is a single continent composed of the subcontinents of América del Sur and América del Norte, the land bridge of América Central, and the islands of the Antillas. Americano or americana in Spanish refers to a person from América in a similar way that in which europeo or europea refers to a person from Europa. The terms sudamericano/a, centroamericano/a, antillano/a and norteamericano/a can be used to more specifically refer to the location where a person may live.

Apparently its a language barrier thing.

Never heard of the term seven summits but the Olympic flag has five rings for the five inhabited contingents.

parts of China in Europe

What a weird way to put it. I'd argue Europe doesn't exist. It's a pureply political distinction. It's just far west asia. Or Eurasia if you want to be a bit inclusive.

Pan-American continent is the same as the Western hemisphere, making the biggest Canada, followed by the US, followed by Brazil, no?

There are four hemispheres; each colocated with halves of two others. There's a Northern and Southern hemisphere, yes, but there's also an Eastern and Western hemisphere; one from the Prime Meridian East to the Date Line, and the other from the Prime Meridian West to the Date Line.

And actually, geographers talk about a third hemisphere delineation: the "Land Hemisphere" and the "Water Hemisphere." The "equator" of this hemispherical division is a circle that runs south from Baja California to just under Peru, curves across South America and across the Atlantic where it ducks under South Africa, then curves back North to skirt just below Vietnam and Japan before turning South again over the North Pacific. That might not sound like a hemisphere, but it is when you look at a globe; and the "Land Hemisphere," which is centered on France, contains 81% of Earth's land, while the "Water Hemisphere," which is centered just south of New Zealand, contains about 63% of Earth's water.

What is Western Hemisphere, Alex?