Would it be okay to write an essay regarding religious trauma? If so, would it be acceptable to include Bible verses?

This would be okay, if it answers the prompt. Colleges would in fact find it interesting to read, and it could add a whole new aspect to the personality you portray in your applications. It's also fine to include some Bible verses.

I think it would be okay to write about that if it has affected you and who you are. I think that you could include Bible verses, but don't overdo it. I wouldn't use too many words on that because those words didn't come from you and don't show who you are as well as your own words.

I think this is a risky topic simply because you don't know who is reading your essay. I think you should still write it so long as you have specific anecdotes that show how this was a unique experience you had with the religion as it's possible if you write too generally someone could be offended by your essay. Although I think you can write the essay I wouldn't quote bible verses because based on the premise it doesn't seem like it would be constructive to do so.