Translation:In the world there are many diverse religions.
after ekzistas why isn't " multaj diversaj religioj." all with accusative "N"
Because "multaj diversaj religioj" is the subject, they are the ones doing the existing.
Try and rephrase it and you will see it clearer:
Multaj diversaj religioj ekzistas en la mondo.
but how do you know that " multaj diversaj religioj." is the subject? Isn't the the subject "there" ?
"there" is not the subject, it is not a noun and can't be the subject, "there" is just a dummy word English uses in this case, if you look at the Esperanto equivalent there is no similar word, because it is enough to say "ekzistas" or "are/exists", you don't need to say "there exists" because the "there" does not serve any function.
If we take away "en la mondo" away to remove any further confusion, as this is not a relevant part of the sentence, we are left with:
Ekzistas multaj diversaj religioj.
Multaj diversaj religioj ekzistas.
Now there is no object in this sentence, we only have two parts to work with: multaj diversaj religioj and ekzistas, clearly ekzistas is a verb so that one is out of the question, thus we are only left multaj diversaj religioj, and as a sentence can't be without a subject, multaj diversaj religioj therefore must be the subject.
A sentence would be meaningless without an object, it would be like the sentence:
Okay now, who or what is eating chicken?
If you ask yourself the question: who is verb-ing? You will have the answer to what the subject is.
If you ask yourself: who is being verb-ed? You will have the answer to what the object is.
In this case:
Who is existing? Who are?
multaj diversaj religioj
thus they are the subject.
La koko manĝas semon.
Who is eating?
la koko (subject)
Who is being eaten?