"Mr. President" is the way you would address the president of the U.S. (or any other country). "Mr. Speaker" is the formal title of the Speaker of the House or the Speaker of the Senate. Each speaker is the presiding officer of each body of elected officials for the U.S.

This is certainly not a slang. It is the proper way to address these people even if you're not having your speech.

But yes, that's what they say!

This is not slang but rather the formal language of American politics.