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DialogFlow sending context back after authentication?

I am having a bit of a hard time wrapping my head around how to connect to my OAuth2 Freshbooks API from my bot. Currently I have my API set up such that hitting the /auth route will take the user to the Freshbooks login page and once successfully authenticated the token is returned back to the user. After we have the token the user can get all of their invoices in my web app.
Now, when I build a DialogFlow bot, how do I go about this? What I have thought about is that the user first hits the /auth route which returns the authorization URL which the user can then open in their browser and log in...but after login, how do I return back to my bot?
After a successful login, the /callback route is called by my api with the authorization code to get the token...but this will not be returned back to the bot since it is all happening in the browser...I think.
What is the best approach for this?
Also, after getting the token from my API, should this be stored in a context in my bot?
Thanks for the help and sorry if this is a beginner question. I tried finding an answer online but I just cant wrap my head around this one.

Assuming that your OAuth service is configured correctly you don't have to worry about any of this. The procedure works roughly as follows:
Account linking is triggered via one of two ways:
If you need a linked account to fulfill a certain intent you can simply check the Sign in required box of that intent in the Google Assistant integrations page in your Dialogflow project. If you check this for all intents that are listed for invocation the user can only use your agent once they have an account linked.
The other option is to manually call the sigin helper. This can be done at any point during the conversation, i.e. it does not have to be tied to a particular intent.
When the account linking procedure starts the Google Assistant will load your login page in an in-app browser.
Once the user has authorized your client the OAuth service should (like any OAuth service) redirect the user back to the client. On the Google Assistant this happens via a redirect url of the format https://oauth-redirect.googleusercontent.com/r/<google developer project ID>.
After that Actions on Google calls your fulfillment service with the original intent (the one that triggered account linking), only this time with a valid access token for your service.
Such an access token will from now on be included in every fulfillment request your receive from Actions on Google. You do not have to store this token, you should always use the one that is send in the request.
For more details see the Implement Account Linking documentation.

Do I need to ask for the artist's permission every session to access his Facebook page status updates?

I need to access status updates of an artist page to display as feed on my website.
So everytime a user accesses the artist' space on my website, he sees the artist's status feed in a tab.
Do I need to ask for the artist's permission every session? That would not be practical I guess.
Thanks

You only need to ask permission once, when the user logins for the first time.
If you use the client side JS SDK, that is really all you need to worry about. The access_token will be automatically refreshed by the SDK whenever needed. The user only needs to be logged in to facebook, no action is required.
You will most likely be using the JS SDK.
So unless you use a manual server side oauth flow, see below:
If you use a manual server side oauth flow you usually get a short-term access_token that is valid for 2 hours after the user logs in for the first time.
You can request a long term access_token by sending a request to oauth/access_token with some additional parameters:
See here:
https://developers.facebook.com/docs/facebook-login/access-tokens#extending
This long lived access_token is valid indefinitely, but may expire at ANY moment.
Reasons could be:
user password change
user logout
use de-authorizes app
...
So you are to just reuse the access_token whenever you want to interact with the users facebook account ( you don't have to ask them to log in again).
But as soon as your access_token becomes invalid, you have to update the acces_token by sending the user trough the oauth flow again.

Facebook: Authorize user on server after successful login on JS

I am using sdk that facebook provides(in java-script), to add login option in my site with facebook. I succeed to do this on client side, but I want to identify this user on server side without php-sdk.
So I need from client side send a request to server, that will prove that (for example) user with ID 1234 in Facebook, indeed logged in to my site. I don't want to use php-sdk, because it's the only time I will use it, so it's seems to me a waste to load all the sdk just for that.

How can Facebook verify Facebook Connect requests?

So I'm developing my own API for my website - I'm mimicking the Facebook JS SDK in regards to how my system works. API client displays a button, popup comes up and the user can log in. Login popup issues an event to the opener window and the parent window now knows the user is logged in. That all works.
What I'm having trouble understanding is how they can verify that the refresh requests are valid. If the API client needs to send a request to the server to ask if the user is logged in and it's all in JS, then everything is transparent. The API client says, "Hi, I'm application 4jhkk2l3bnm389, is the user that's logged in on Facebook also authenticated with me? If so, can you send me a new token so I can make API calls?" and Facebook says, "Oh, you're application 4jhkk2l3bnm389? Yeah, the user is logged in and has allowed you to access their information, here's an access token."
But how does Facebook prevent an outside application that isn't the authentic application from saying, "Hey, I'M actually application 4jhkk2l3bnm389, I promise I'm not lying. Can I have an access token?"
I have no idea how they determine the difference. Obviously if it was all done through AJAX calls in modern browsers then you could just provide an Access-Control-Allow-Origin header. But if a malicious client were to use cURL then I don't think I could ever tell the difference. How does Facebook do it? A good explanation is much appreciated! Thanks!

All access tokens belongs to an app/user pair, and in order for Facebook to return such an access token to the app, these has to be verified.
The app, or client_id, is verified against the domain specified in the redirect_uri - if the page tries to use a client_id/redirect_uri pair it does not own, then it will not receive the access token as this will be passed to the valid redirect_uri (the mechanism the JS SDK uses follows the same rule).
The user, or uid, is verified using the cookie Facebook sets when you sign in.
While you can easily spoof the client_id/redirect_uri pair using curl, the same does not apply to the uid, as you would have to be in the possession of the users cookie. And if this is the case, well, then you could simply grant your own application access.

Facebook uses OAuth 2.0 for authentication. You can find details of how Facebook deals with OAuth right here: https://developers.facebook.com/docs/authentication/. There are many different ways OAuth can be used, depending on whether you're on a mobile device, a page on facebook.com itself, or, in your case, just a web page outside of facebook.com. The details of that final flow can be found here: https://developers.facebook.com/docs/authentication/client-side/.
Basically, Facebook knows what applications you have given permission to view your information. When you run one of those applications, they first make sure you are logged in to Facebook, then they request a user access token from Facebook, essentially saying, "Hey Facebook, I don't know this person, nor should I. Can I get access to their information?". And then Facebook looks internally and if it decides this particular application should have access to this user's information, it sends a user token.
That's the simple way of describing it. There are many different ways the authentication flow can happen, depending as I said earlier on what kind of device the request is happening from, whether this is a page on facebook.com, etc., essentially based on your security constraints. Best to read the Facebook authentication docs referred to earlier for the details since it can get quite tricky.

Is the Facebook JavaScript API suitable to create user accounts?

I want users to be able to register on my mobile (web based) app and login using their Facebook account. Is this possible using the JavaScript API?
The user can login using Facebook, and the userID and auth code of that user can be sent to my server to create the account, but I see a security flaw because then anyone could then log in as anyone by sending a userID and their own auth code. So can user accounts not be done with the JavaScript API and only with a server side API?

All Facebook requests are also signed with a secret key that belongs to the app you've registered to handle Facebook sign-ups on your website, so you can use that to verify it comes from Facebook and not someone else.
This is also outlined in the registration documentation

Strictly speaking, it is not possible for the Facebook SDKs to explicitly create a new user. However, when you implement a 'Login with Facebook' button (see here for JS and here for PHP), Facebook's OAuth dialog appears, which will prompt the user to log in (if they are not already) or to sign up with Facebook, thereby creating a new account, albeit not under your control.