I'm trying to work out the above question and I'm not sure if "where" is the best word to use here? I.e. I'm trying to say: for what purposes would a painter benefit from science and scientific thinking.
I agree with Starfrown (this is getting to be a habit). I'd be more likely to say something like Why would a painter ever need science? or, a more informal version, What would a painter do with science?
I also agree. I. personally, would choose "when" rather than "why" - "in what circumstances", if you like, rather than "for what reason". But there's little to choose between them and I think it is largely a matter of personal preference.