Is "Their book already is here" acceptable? I think it's functional English, but the emphasis might be different to the Russian sentence
As a native English speaker that sounds very awkward to me. "Their book is already here" sounds much more natural.
I'm mentally putting emphasis on the "is", as though it's said in response to a question. But I can't really think of any examples, so I might have just made up some grammar rules in my head :)
for what it's worth (3 months later), what you've said makes sense, and you're also right in that the emphasis is likely different to the Russian.
"Their book already is here" sounds pretty strange in English. "Their book is here already" would be an acceptable variation, though.
Edit: I realized my previous explanation was incorrect. Basically, some adverbs can not be placed in front of verbs in many situations.
Can this mean in time (as in just recently available to buy) as well as in physical location?
In Engish, yes. "Did their book come from Amazon? Yes, their book is already here." No one would say this though. We'd answer with one word, "Yes."
I thought the н in них is dropped when following a preposition, but here it is dropped at the beginning of the clause. What are the rules for dropping the н?
You've got it backwards. The "н" is added when following a preposition. Also "н" is never added to "его", "её" and "их" when they are possessive pronouns: "his", "her" and "their" respectively.