Hydrogen is purpose-built to be used for custom Shopify storefronts, correct. So you're communicating with Shopify's backend using helpers like `useShopQuery` https://shopify.dev/api/hydrogen/hooks/global/useshopquery
As for hosting, you can deploy to Shopify's Oxygen platform (Worker-based), or any other deployment platform that supports Node.js or v8 Worker runtimes.