why not: "what did zofie hold by those strange instrument?"
THOSE is plural, while the instrument in this sentence is not. So you need THAT and it would work
In English we don't say "hold BY that instrument," but instead say "hold WITH that instrument."
What would be the structural difference between this sentence and the translation for: "What was that strange tool žofie was holding?"
In the original sentence, Žofie had a tool and was using it to hold something else, while in your translation she was just holding the tool.
"What was that strange tool Žofie was holding? = Co byl ten zvláštní nástroj, který držela Žofie?"
would the sentence be correct without tím?
Co držela Žofie zvláštním nástrojem?
Or is it one of those words that dont't have a meaning on their own, but rather only exist in a certain context?
The Czech sentence without the demonstrative would be OK, but no matter how I read it, it always corresponds to the English one with "a tool", so I do not see it as an OK translation.