In-Process API not returning User join date and last visited date.

No authentication codes should be needed when accessing the in-process API, because it is expected to be used when compiled into the integrated app environment.

While it can feasibly work, usage of IHttpHandler is not recommended.  The appropriate way to handle these is raw urls
https://community.telligent.com/community/11/w/developer-training/65062/page-definition-and-url-routing

I would also highly recommend you make use of the User REST API since it is working with the way you've set up your environment. If you'd rather define a custom REST API to re-expose the internal userApi calls, then this is the appropriate way:
Exposing Data to External Sources 

Steven, Thanks for the information. I tried the custom page URL. If the user logged in to the community they can able to view all the user info. else it's the same issue.
Now I worked on Exposing data to an external source. My extension not displaying Administrator-> extension section. Can you please help why it's not registered in Telligent?

public class SampleRestEndpoint : IRestEndpoints
    {
        public IEventLog eventLog = Telligent.Evolution.Extensibility.Apis.Get<IEventLog>();
        public void Initialize()
        {

            eventLog.Write("init rest", new EventLogEntryWriteOptions());
        }

        public string Name { get { return "Sample Rest Endpoint"; } }

        public string Description { get { return "Sample Rest Endpoint Description"; } }

        public void Register(IRestEndpointController restRoutes)
        {
            eventLog.Write("register rest", new EventLogEntryWriteOptions());
            restRoutes.Add(1, "test", null, null, Evolution.Extensibility.Rest.Version2.HttpMethod.Get, (IRestRequest,HttpResponse)=> { });
        }

    }