Facebook need an account to use its features. You can also use it's marketplace to run your business. To start your business, you have to make a personal account then attach it with your business page to sell or buy New products. If you are not able to login Facebook marketplace, then make sure you enter the correct user's credentials and also check internet connection. If you are still unable to login, then talk to Facebook customer service to get an appropriate solution. https://www.customercare-email.net/facebook-customer-service/