They're not roots, they're mycelium. The mushroom part is just the fruit. The main part of the fungus is the mycelium. It's the mycelium which absorbs nutrients from the growing medium - they can't manufacture their own food by photosynthesis like green plants can.
Mushrooms don't need to be kept in the dark - in the wild they grow in fields. They need cool and damp to fruit all year round rather than just in autumn, and this is easier to provide indoors - but there's no need to spend money on lighting.