Translation:There are eight desks.
八つ "yattsu" is a counter that specifies 8 pieces of whatever thing you just said. Those counters are used every time you need to specify an amount and there are different counters for different types of objects. Their pronunciation is also unique and different than the plain number words (八 "hachi")
Different meaning altogether.
I think of it this way:
あります = (it) exists
です = (it) is
A thing can "be" (です) without specifically "existing" (あります). For example: "The desk is (です) small." vs. "A small desk exists (あります)."
You use あります when you otherwise wouldn't know the thing exists at all. You use です when you already know the thing exists and you just want to say something about it.
Example 1: Your mother is on the phone asking what your dorm room is like. You say, "つくえがあります." But if your mother is visiting you, and you're showing her around your dorm room, you say, "つくえです."
Example 2: You have a chair with a fold-out desk hidden in the arm rest. You show your mother what looks like an ordinary chair and tell her, "つくえがあります." Then you fold out the arm rest to show her how it works, and you say, "つくえです."
Using を would have made the sentence ungrammatical because あります is an intransitive verb.
が indicates that つくえ is the "subject" or the "agent", i.e. the thing which is doing the verb. On the other hand, を indicates the direct object of the verb, i.e. what the verb is being acted upon.
You can't "exist" something; it does the "exist"-ing by itself.
Because there's nothing about "over there" in this sentence. It's just:
つくえ (desk) が (particle) 八つ (eight + generic counter) あります (there are)
Your sentence would be 八つのつくえはあそこです。Here, we have:
八つのつくえ (eight desks) は (particle) あそこ (over there) です (copula, most similar to English "are" in this sentence)