A quotation that shows the motif of racism in chapter 27 is when Bob Ewell shouts at Mr. Link Deas, "I ain't touched her, Link Deas, and I aint about to go with no nigger." Clearly, Bob Ewell's racism is evident in this quotation and it also helps to escalate the situation you mention in the second part of your question.  

As for how Bob Ewell escalates the Tom Robinson/Atticus Finch situation, here is a numerical list of the events:

1. He loses his job for being too lazy, but tells the welfare lady that Atticus "got" his job. He is essentially accusing Atticus of somehow causing his firing from his job.

2. Judge Taylor, the judge on the Tom Robinson case, sees a shadow on the corner of his house. It is assumed that this is Bob Ewell's shadow. The screen of the back door was also cut. 

3.  Helen Robinson can't use the public road to work because Bob Ewell "chunked" at her when she walked by his home. 

4.  Once Mr. Deas tells Helen to use the public road, Bob Ewell follows several paces behind her "crooning foul words."

5. Finally, as mentioned above, he has a brief screaming match with Mr. Link Deas in which he calls Helen a nigger; he does, however, stop following her after this altercation.

Atticus and Aunt Alexandra discuss why Bob is doing these strange actions, and Atticus decides that Bob expected to be hailed a hero after the trial. Instead, all of Maycomb knew he was lying and he was sent back to his normal, everyday life. Atticus expects him to settle down once the weather changes, but we know that Bob does not. Eventually, he attacks Atticus's children, and they are saved by Boo Radley.