From Revelation 12:9, we know that the dragon is Satan, the devil. Satan has a mouth and is an individual.
The beast in Revelation 13 is not called a dragon. So the first beast that has a mouth of the mortally wounded/healed head that blasphemes God is not Satan, but a different person.
There are three mouths, of three individuals, in Revelation 16:13.
You have mistakenly identified the false prophet as the one ruling the world. So you can't identify - an individual person - as the beast, who has a mouth.
It is the first beast, the mortally wounded/healed head, who the false prophet has the image made of - the abomination of desolation - who will rule the world, who is the beast in Revelation 16:13 . And in Revelation 13:5 who has a mouth "speaking" great things and blasphemies.
Just as the little horn person speaks great things in Daniel 7.
Revelation 13:5 And there was given unto him a mouth speaking great things and blasphemies; and power was given unto him to continue forty and two months.
Daniel 7:8 I considered the horns, and, behold, there came up among them another little horn, before whom there were three of the first horns plucked up by the roots: and, behold, in this horn were eyes like the eyes of man, and a mouth speaking great things.
The correct identification is...
1. the dragon - Satan
2. the beast - the little horn person
3. the false prophet - a spokesman for Satan and the beast person.
In your Nazi Germany comparison, it would be...
the beast - Adolph Hitler, speaking great things
the false prophet - Joseph Goebbels, propaganda minister