The Americas is what you mean, vs America, which implies the US. If you want to include Canada and Mexico, you say "North America". It's not difficult.
I've been all over the world, and no one has ever been confused when I say I'm from America. This push to make it seem like it's confusing is ridiculous.
Democracy is an umbrella term. These are the types of democracy the US is:
Representative Democracy
Constitutional Democracy
Presidential Democracy
Liberal Democracy
Types of Democracy the US is not:
Direct Democracy
Parliamentary Democracy
Illiberal Democracy
Participatory Democracy
Social Democracy
So yes, it's a democracy.