I would suggest that "Not one of them is here." and "None of them are here." to be two of the most accurate translations for this (as speaker of British English), but it seems that "None of them is here." is offered as the best translation. This, to me, sounds a little strange (as if the subject does not agree with the verb).
Just my own, personal opinion.
"them" is the object of the preposition "of." The verb agrees to the singular subject "none." The trick I learned regarding prepositions and verbs when learning subject-verb agreement is to completely remove the preposition/object of preposition and see if the subject-verb relationship still makes sense.
This is wrong in this instance. Them implies that the "none" refers to discrete individuals and not something that is uncountable. You could say "none is here" if referring to something uncountable like flour for example but not when they are countable and individual as "them" implies.
As a native British English speaker, "None of them is here" is wrong because just before, 'is' you are saying 'them' which makes the 'none' plural, like 'none of the 3 people are here'.
For 'is' to be correct, 'them' would have to change to 'it', 'None of it is here', for example, 'None of the (one, single...) cake is here'.
Many English speakers say 'is' when they should say 'are'.
'None' can refer to singular or plural, the use of 'them' instead of 'it' made it plural, which means that, 'are' is the only correct word to use in this sentence if 'them' remains unchanged.
In actual usage, the word "none" seems to be used both ways. When "none" has a singular referent, it's always treated as singular; when "none" has a plural referent, it's usually treated as plural but sometimes as singular. I found this page with more information: https://english.stackexchange.com/questions/1425/none-as-plural-indefinite-pronoun
I'm guessing "żadnego z nich" is in the accusative because of "ma"... so if I wanted to say something like "none of them like apples", would "żaden z nich nie lubi jabłek" be correct? (given the preferred English translation, I'm assuming the Polish sentence would take the singular?)
Starting from the end: your sentence about apples is perfectly correct.
Now, to the Accusative thing... no, it's Genitive. "mieć" (to have) takes Accusative, true. But it's negated here, and negated Accusative = Genitive (don't forget that it's the only case that changes when negated).
Also, as the word "żaden" by definition is a negation, and negated Accusative = Genitive... it's very very rare to use "żaden" in Accusative. I guess it only can happen when Accusative is needed by a preposition, not verb (it doesn't change then). So, for example "Nie czekam na żaden stół!" (I am not waiting for any table!).
Sounds unnatural. "There is none of them here" is what you want. One can, however, imagine a situation in which your phrase would be appropriate. Say, you are looking for 3 friends of yours, and you are expecting to find one of them behind the curtain. You are about to draw the curtain back, and begin announcing "Here is... ". You draw the curtain, and there is nobody there. So then, you could finish by saying "...none of them!"
Hmmm, this one was really ❤❤❤❤❤❤❤ me up and I think I've figured out why. In the english sentence "none of them" is the subject, while in the polish translation the subject isn't specified and if I'm understanding correctly (and god knows I might not be), could be more literally (if awkwardly) translated as "It does not have (or there is not) any of them here". If that's the case, might it be a good idea to change the english translation (or at least the first option if you already accept it) to "There is none of them here" or something like that?