Does zij here refer to people, or could it refer also to objects?
My current understanding is that to refer to objects it would have to be
wat zijn het precies
Correct. "Zij" must refer to people. Objects must be referred to as "het".
If it is referring to people, than why does it say "Wat" and not "Wie"? I have run across many sentences that do no accept "Wat", when referring to people.
Same as in English: "What are they" = "Wat zijn zij", "Who are they" = "Wie zijn zij".
Even if it is in plural?
Then it would be "wat IS het precies" for things and "wat is hij/zij precies" for people (with "zij" third person feminine singular).
How about "Exactly what are they?"
Well in English that is about the same as "What are they exactly", right? So I think this would translate fine.