I don't know if they are common there is no verb for Race, racism is the noun and racist is the adjective so for grammar corrections.
1) She is being racist toward the guy in class. correct grammar.
2) There are many people being racist toward black people in the US . I think you made a spelling mistakes with 'are bring'?
3) He was experiencing racism by a girl in his class. A girl in his class was being racist toward him.
4) He always talks about how racist she was whenever he meets people.
5) I do not know why black people usually feel like other people are racist around them.
Maybe someone with more experience in this area can add better comments.