Is damnation appropriate to say in an essay if you are referring to it in a biblical/ religious sense?

Depends on the context. I once asked God about the word 'damned' in a reference to lies. Within just a few hours He showed me that there is indeed a place that the word is appropriate to use.

Damnation means " the state of being in hell as punishment after death". So it means the person is already in hell.

The act of condemning someone (to hell or other) is called condemnation.

I'll tell you what, I write about how people are damned all the time. They get damned for cussing, damned for fornication, damned for stealing... you'd be amazed how many damned people are out there.

Yes, but if you prefer, you can substitute "condemnation" instead.

condemnation