There isn't a limit to how many different projects you can host, as long as you can pay for them you can host as many as you want.

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Unfortunately, Railway added a limit of 2 custom domains per service, leaving you with three domains total; 1 is the Railway-provided subdomain and then you can add 2 custom ones. You can increase this to a soft-limit of 10 by upgrading to pro plan.

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You can deploy a Next.js app with a MySQL database in hobby plan, Railway provides database services for your app to use and MySQL is a provided one, you can right-click on your project and click "Add Database" and "MySQL" should be an option, read more on that here: https://docs.railway.app/guides/mysql