Translation:This is the director whose shoes I have bought.
What's worse is that that is just a normal duolingo sentence
Can this be reformulated to "Dit is de directeur van wie ik de schoenen gekocht heb"?... Or is there a reason it is wiens and not van wie? Are the masculine and feminine the same, if I never use wier?
There is a slight difference, grammatically at least. Your suggestion would translate to: "This is the director from whom I bought the shoes". It doesn't describe the ownership of the shoes, but rather the person who you are buying them from. Perhaps someone stole the director's shoes and is selling them on the black market!
"Wier" is traditionally the feminine form of "wiens", but it is going out of use. Most native speakers these days will use "wiens" for masculine, feminine and plural. See here for more info (in Dutch).
I guess you could say "voor wie" or "van wie" instead of "wiens" in this sentence, because "wiens" could mean two things: you either bought new shoes for him, or you bought his shoes for someone else. If you use "voor wie" or "van wie" instead, the meaning would be much clearer.
That is correct, but if you were to use 'wiens' in this sentence, people would generally understand it to mean 'van wie' without any further context.