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Using IdentityServer4 as Class Library instead of Hosting Solution

I have been exploring IdentityServer4 for a couple of days. It performs hosting internally generating a connect/token endpoint which internally validates and generates an access token.
Even to call it a discovery URL is needed ultimately requiring a web app template for hosting.
Is it possible to use IdentityServer4 as a library that just allows access tokens to be generated?
**Updated Based on input from Bryan
What I am trying to achieve here is GSMA Compliance that requires both OpenID Connect and OAuth. I need to generate an Access Token as well as Identity_Token. But the caveat here is that IdentityServer4 hosts its internal endpoint where I do have custom endpoints. Also it require http based calling and I do require a sort of library that I can integrate and internally call to generate Access token as well as Identity Token.
** Some more update
We have hosted a custom GSMA compliant Web API Project and have hosted several endpoints as per required by GSMA ultimately validating and sanitizing the request landing on our endpoints. Internally we do require an Access token and Identity Token to be generated and shared back on the callback of the calling party. Currently, I have used an Identity Server template which is MVC based project ultimately requiring us to use at least two ports/project one for our Custom GSMA compliant APIs and one for Identity Server. Calling identity server via URL add a new hop and an HTTP request needs to be sent out to Identity Server whereas I was thinking to use IdentityServer as a class library somewhat allowing me to pass in input parameter and do get an access token/ identity toke.
Upon dissecting server Identity Server project like
Identity Server 4
Identity Mode
Identity Storage
I got the impression that it's very difficult to exact a library out of these projects that can help me generate access token/identity token easily.

IdentityServer4 is an OpenID Connect (and OAuth) identity service -- it's not just about tokens. Those technologies are primarily HTTP-based. Thus IS4 is built on top of ASP.Net Core's web tech. If you just need tokens (JWT, I assume), it's pretty simple to roll your own and use them however you see fit. A few Google searches (or an SO search) will provide you with the code needed to create your own JWTs (for example: https://houseofcat.io/tutorials/csharp/identity/createjwt). Without more information about how you want to use them, I can't elaborate on this answer.

Implement identity server authentication in real world scenario

I am investigating how IdentityServer 3 works and I still have problem to fully understand.
In general concept is clear to me but still I am not sure how to implement this on real project.
This is basic example that I am trying to implement in my case: link
I have web api project and I want to call my api methods from any client (mvc, wpf, phone…)
So I need implementation that is suitable for all clients.
If I understand well (and probably I am not understand completely), I should have 3 projects:
Client
Api
Project that host IdentityServer
And all projects should have required stuff like on picture:
Steps on picture:
Get token
Return token
Call api
Check if Token is OK
If Token is fine than return data else show error
My questions are:
Is my thinking about how this works ok?
Where I making mistakes?
Is this example good enough for my case? Am I missing something
important?
Do I have to create project that host IdentityServer, or this is
needed just for example code ?
Does IdentityServer host project must be console application that
communicate with api and client(like in example), or in real world
this is done differently ?
Should project that host identity server be aware of Clients and
Users ?
Should some other project except host identity server project be aware of Clients and Users ?
What is diference between implicit and hybrid flow, what I need in my case and why?
How do I create my own login view? I want have html page for login if I use web client, but to have wpf login view if I use wpf, also different view for mobile client.
EDIT:
I think that I need Resource Owner flow . I supose that resource i view where user type user name and password.

Your basic flow is correct, with Identity Server acting as your authorization server and your client and web API separate.
You should host Identity Server in its own project to ensure it is separate from any other logic which has the potential to introduce security concerns. How you host it is up to you and your use case. Typically you would see it hosted within an ASP.NET project on an IIS Server.
Identity Server must be aware of clients and users in order to authenticate them. The only other projects that should be aware of your identity store (users) is any applications that concern things like admin, user registration, etc. The client store would only ever be used by Identity Server.
Views can be modified using the Identity Server templates or by introducing your own ViewService. See the docs for more info: https://identityserver.github.io/Documentation/docsv2/advanced/customizingViews.html
Regarding flows, the Resource Owner flow is OAuth only, so there will be no authentication (log in page), only authorization (server to server).

Security between .NET MVC and WEB API

We are starting a project which will consist in:
Web project (ASP.NET MVC)
IOS app
and both will consume data from a .NET WEB API service.
The WEB API service will expose a POST Method with the url "user/create". But i don't know how can i avoid another apps for making post to this url? I know i need a security protocol, but i wanted to know which one you recommend me, and if you have, an article where is it explained.
Thanks

web api 2 provides oauth authentication. You will need to get a token from the token end point of web api and pass that token in subsequent requests.
You should find lot of online resources if you search for web api 2 oauth.

We did something similar recently using OWIN OAuth 2.0 Authorization Server
Reference this ASP.NET page for details. Sample code is included as well for several different implementations.
For our purposes, we used the Client Credentials Grant section about half-way down the page. Our implementation involved server-server OAuth (Web API to MVC), but I bet it's pretty similar to have iOS connect. The only thing I would caution is to somehow encrypt the login credentials on the iOS side, and I'm sure there is a way to do that.

So you want the WebAPI to only be used by the MVC page? The best architectural method is to separate the two rather than leave both in one project. Why? Because the MVC app is a experience layer for humans. The WebAPI is an experience layer for the MVC app. Move it back where it can't be accessed.
You can add on tokens, etc, but the MVC app sits on the server, but is accessed on the client computer. The wider the scope of the application (ie, intranet or internet or something in between?), the more difficult the problem and the harder it is for your users to access the application. Moving the WebAPI internal and leaving the MVC app exposed guarantees external users cannot use the API.
The main reason WebAPI and MVC exist together in a single project (still a mistake in most instances, IMO) is you are exposing both to the same audience. If that is not your intent, don't do it.

How to check an ASP.NET MVC user is authenticated and authorized from a separate WCF service application?

I have two projects:
An ASP.NET MVC 5.2 Application using ASP.NET Identity 2.2
A WCF Application SOAP XML service.
Note: The WCF service is not hosted by ASP.NET, nor is it running in ASP.NET compatibility mode. A requirement of this project is that it is interface based and ASP.NET compatibility mode does not appear to allow an interface based implementation.
The ASP.NET MVC Application calls the WCF SOAP XML service server side when a user makes a specific action request. However, the WCF service is accessed via the public Internet so in theory anyone could call it if they knew the address. I need to ensure that only ASP.NET Identity registered users who are Administrator role are able to call it. The WCF Application could directly access the database but it doesn't seem like it would be the best solution?
How can I check from the WCF service whether a user is authenticated and authorized in ASP.NET MVC 5.2 using ASP.NET Identity 2.2 using object passing? Which objects or properties should be passed and checked? Is there any other solution? Is it possible to check authentication/authorization with attributes in wcf?

Do you own both, are they in the same domain?
You could interact with a database behind the scenes to generate an auth token, then have the wcf service pass a url with the token back to the user. When the user goes to the site via the tokenized url it checks against the database from the perspective of the ASP app and authenticates. It's a bit asymmetric, but it would handle your use case without getting into domain restrictions.

Passing user identity from MVC to Web Api

I have an MVC application using Windows Auth which consumes a Web Api service. Both are hosted within the same domain but sat on different servers (MVC is publicly accessible). Now lets suppose the Web Api service has a method "CreateFooBar" which requires that the user is in a particular AD group. At the MVC layer I can easily check that the user is indeed in the group, package up a JSON message and call "CreateFooBar". But how does the service perform such a check? How can I tell it which user has made the request?
Initial thought is just to add the userID to the JSON message and let the service method retrieve the details but this would allow someone to just pass in any userID they like so clearly this won't work. Can someone point me in the right direction please?

You should use something like Kerberos delegation.
The user will be authenticated in the MVC application using Kerberos then the Kerberos token will be passed to the Web API call.
We do that currently at work to pass credentials from an ASP.NET app to an Exchange Webserver. It works fine.
If you want more info check this KB: http://support.microsoft.com/kb/810572

You should look into what windows identity foundation can do for you. By setting up adfs in your environment and using claims you will address most the problems you are talking about.
you'll need the identity and access plugin for visual studio and you can test the idea out using a self hosted sts.