"There are nine desks."
あの・その・この would be "that-(far away)", "that-(near)" and "this-(here)"
あのつくえ would be "that desk/those desks"
so あのつくえがここのつあります is more like "Those desks, there are 9 of them"
There are no specific desks being pointed out, just that nine desks exist so clarifiers like あの are not necessary
は and が in this situation only really differ in showing what information is stressed in the sentence, which isn't clearly stated in the english translation so it really shouldn't matter and both should be acceptable. I'd report it.
With は being like "(as for the) desks, there are nine of them", where the number is stressed, and が being "the desks (are what) there are nine of" where the object is stressed.
The counter form with つ is used only for 1-10 (ひとつ～とお）.
After that, you need to use different counters. It changes depending on what we count. For desks (office desks and school desks), we normally use だい (台: dai). So, 238 desks will be 238だい. Of course you can use だい for 1-10 desks, which is いちだい、にだい、さんだい... By the way, in order to count tables, we use きゃく、き、or たく.