I don't know what to do regarding Auth. Please help!

The whole authorization will take place in the frontend (user logs in with his google account, gives permission to your app, yada yada). In the end, you will receive an token from the "Firebase Frontend SDK". Then you make a call to your own backend together with the token and then use a "Firebase Backend SDK" to verify the token. Once it is verified, you can take a look at the contents of the token, and viola, there is a user id! It will be something like "google:123348436" or "github:138523". Use this id in your custom database.

Firebase has an SDK for .NET Platform , Just verify the Token in the backend which will provide the user id. Save the user in your database against this ID

really have to recommend against doing this yourself. It's rife with security vulnerabilities and just gets more and more complicated. Here's a related article.

Oh wait, I didn't see that you were using C# Web API.
I usually work with PHP backend, and how I handle it usually by validating the input first
say you authenticate with email and password. I will create a function to validate:

1. if email and password exists in the request
2. if email and password is not empty
3. if email is valid email
4. if email is exists in database
5. get the data from database
6. check if password from database is matched with password from user input
   validation passed. now run function to create token/just let the user login

is this the type of answer you're looking for?

(By the way, just yesterday, I created screencast about login, i think it may help you. It's written in PHP, though, but the concept is the same. https://gum.co/funphp )

No, there is no need to use different servers for it. I investigated this issue pretty deeply and in most cases, there is no need to use anything like that. You still can implement 2-servers architecture but it's up to you, no necessity here.

These can definitely just be different endpoints on the same server.

You don't even need JWT.

Client:
/POST users with Email & Password
Server:
creates a DB entry with hashed and salted password, generate and save to DB an auth token which is essentially just a random string of characters (for example use bcrypt hex). Server sets a server only secure cookie with the auth token value

For each future request check whether the request has an authorization cookie and if so use that cookie to get the user that made the request.

Logout is a request to the server that clears the cookie.
Being logged in is a successful fetch the current user from an endpoint.
Login is giving an email and password, the server checking the salted and hashed sent password matches the DB entry and then sets the auth token cookie

You would grab the UUID of the user in Auth0 and assign that value to your business in the db. This is how I do it for one of my projects where I don't need a robust relationship between users and data. (SmashNotes.com)

In another project, I experimented with a "local user," and every time a new user logs, I just create a new account for them:User.create(auth_id: [auth0_uuid_param]). Then, I let Auth0 take care of all the hard stuff, and use this local user only for setting local account permissions, stuff like your payments plan, how many credits you have. (ClipGain.io)

ps. Auth0 has a permissions and access API, but it's a bit more involved and for most basic things I just use a local user account. Look up their "Management API" if you are curious.

yeah auth0 doesn't well support permissioning and access control, so thats problem there, however that's something that authorization SaaS like Authress solve.