is spreading a fake news or smearing hateful propagandas a right one can exercise under freedom of expression? Explain

No.

Explanation:

Most of the speech in United States is protected under the first amendment of the constitution. But if we let other people say anything they want without repercussion, there will be some cases where the freedom of speech can be exploited.

This was the reason why The Supreme court of United States created several exception for this :

obscenity,

fraud,

speech integral to illegal conduct,

speech that incites imminent lawless action,

speech that violates intellectual property law,

true threats,

and commercial speech such as advertising.

Speech that contains any of the things above can be subjected to further legal case depending on how much damage that speech created.

slavery, abortion, donald trump, gay marriage, racial rights, immigration  

explanation:

anything that has been broth up to the supreme court is something of grate political divide   so just look as court cases