Would it be possible to make a microscope on the island using just a basic array of wire, glassware, kitchen utensils and a car battery but not a clean glass lens in sight?

How does a microscope work?

Essentially, a microscope is just a lens. You can see the principle quite easily by looking through a tiny drop of water. Try balancing a water droplet on a 2mm hole made in cardboard and looking through it. You'll have to get your eye very close - and the object you're looking at very close too - but it magnifies surprisingly well.