If "z" means "with", yes. But it can have some other meanings, most importantly 'from' (from somewhere / made from something) and that takes Genitive.
Could one say
"Oni nie są żadnymi artystami."
If so, how would it differ in meaning from "Oni nie są artystami."?
Yes, that is correct.
"Oni nie są artystami" simply means "They are not artists"
Adding "żadnymi" suggests that either 'they' themselves or your interlocutor claims that "they are artists", and you consider that statement total BS.
So to get this straight, we change 'z' to 'ze' prior to a word beginning with 's' or 'sz', but not 'ż' ?
ż as well, but generally the rule is for words which start with a cluster of two consonants, first of which is z/s/sz/ż and similar. 'żadnymi' has just one consonant at the beginning.
Both look fine, with just a small nuance of difference between them... I would say it this way: "Boss, there are two artists here ready for work! - We are not working with any artists! / Boss, there is an artist here ready for work! - We are not working with any artist!"
This is more of a general question but i have a lot of trouble hearing "z" in a sentence, particularly when the next letter is also a z. Is Duolingo reflective of how it would be spoken?
Well, it sounds pretty clear to me and it generally should be clear. If the next letter is also a "z" (here you have "ż"), it will kinda make a double "z" sound.