Close. But it's not (re)named Lake Americas. Remember, there are two continents, North America and South America. It's not one continent; however, jointly they can be called The Americas.
Sure, and referring to the whole of the UK as England is also a thing. It’s confusing but people are people. Or as they say in some parts of “England” it’s queer as folk.
If you follow the link there are dictionary entries. It's not stupidity, it's completely reasonable. Amerigo Vespucci didn't name the USA, he named the entire continent.
"Britain" is widely used to refer to the UK, but Great Britain is the physical land mass which excludes Northern Ireland, so there is rarely confusion.
Not yet, but I assume they will. They said they only ever show the official names designated by the country in question. Probably because a lot of countries disagree on borders as well as names and get really upset with people who get it wrong.