Does pyrite retain the magnetic properties of its element iron?
Pyrite is not magnetic. Some related minerals are, but only weakly, not as strong as iron, so the test will likely fail anyway. Magnetism is not an inherent property of an element, but that of a compound. Most compounds of iron are not magnetic (though some are); on the other hand, there are organic magnets made out of totally non-magnetic elements.

Think of something based on chemical properties instead. Pyrite is a salt of a metal and a weak acid. Gold is a metal, of the kind that would not react with acids. See where this gets you.

As for the other properties of the elements, some would be inherited by their compounds and some (arguably, most of them) would not.