Login and Authentication System

The Cloud offers different services to manage an authentication system without building it from scratch, for example AWS Cognito or Google Firebase:

We will assist you in you in making the best service choice, as well informing you of the best practices to build one.

FAQ

What tools exist for authentication? How about OAuth2.0?
I want to avoid building a system from scratch, how can these tools help me save up development costs?
Which additional authentication methods are available? (2FA, SMS, password...)
How much does it cost to store thousands of user, when I scale?
How should I handle user data, making sure it is protected and privacy is assured?