Should I include challenges I faced on account of my caste in my diversity statement?
Your diversity statement is not about who you are.  It is about why you should be admitted to the degree program.  In particular, it is about your ability to work with other people in the degree program and your later career, and how this ability will advance the goals of the degree program.
If your experiences relating to your caste has prepared you to work with other people, including perhaps disadvantaged people, then yes, write about that in your diversity statement.
The fact that there are upper caste faculty in the department is not very relevant.  Faculty overwhelmingly come from a higher status background than applicants.  There will be many applicants discussing experiences that are unfamiliar and uncomfortable to faculty.  Avoid stereotypes and personal attacks.