No. If you democratically elect terrible representatives who eat puppies, it's still democratic.

> Also, what about federal judges? None of those are democratically elected, and they get to interpret all the laws in ways that have great consequence.

You don't have to elect every government official for it to be a representative democracy. Democracy means that the ultimate power is vested in the people. If you elect representatives who appoint judges, the judges are still appointed by the power of the people.

> Hence, America's government is a little more complicated than "democracy", although some parts of it are surely "democratic" (e.g. the house of reps).

No government is simple. America is very clearly not a direct democracy, nor are all officials elected, but it is still a democracy.