That we can, from a piece of art, (i) ______ the unconscious urges of the artist— urges that remain hidden even from the artist himself— will remain a( n) (ii) ______ issue, as it is one (iii) _______ empirical analysis: we can never definitively know what is submerged deep inside the artist’s psyche, let alone reconcile any such revelations with the artist’s work.

For blank 1, the biggest clue is "urges that remain hidden even from the artist himself" - indicating that from a piece of art, we, as viewers, are able to understand or deduce these urges, which remain hidden to the artist himself
=> "derive"
However, lets look at other options:
"appreciate" - comes close in a +ve sense, but if you look at the context we are not talking about art appreciation i.e. whether one is able to appreciate on or not, rather we are talking about someone who can understand the meaning of the art, and in a way understand the emotions coming from the art (probably someone who already appreciates art)
"subvert" - opposite in nature to what were expecting i.e. -ve

For blank 2 & 3 hint is within "we can never definitively know what is submerged deep inside the artist’s psyche, let alone reconcile any such revelations with the artist’s work."
takeaways: we cant fully know all these urges nor justify how we are able to understand these urges emanating from the painting

For blank 2 we are looking for a word which means not easily understandable, mysterious etc. => best fit is "intractable" (other 2 options "practical" and "unambiguous" are basically opposite to what we are looking for)

Whereas for blank 3, we are looking for a word which means - we cannot explain with (empirical analysis). Best fit is "not readily amenable to" and same as in blank 2, other two options are exact opposite - "easily subjected to", "likely to be resolved by"