Does which slur was used really matter? A slur is a slur, it's just hate speech. Which particular racial slur is probably irrelevant. Given previous occurrences this year already and the girls in the article pictures are black, I'm sure we can probably guess. If your kid was the target of the statement, would it really matter to you which word they used to insult and degrade them? To answer your other questions:

The raised fist is a globally recognized symbol of solidarity against oppression.
https://www.nationalgeographic.com/history/article/history-of-raised-fist-global-symbol-fighting-oppression

"Hate has no Home Here" is a non-profit group from Chicago that is trying to combat hate speech.

https://hatehasnohomehere.wordpress.com/about/