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WiFi Communication C# and ESP8266

I'm working on a project and am looking for a way to connect with ESP8266 via WiFi module on ESP8266. I have to build use this method, through the windows desktop I can control the movement of robot. From C# to ESP just like remote control project. I have a lack of knowledge of C# same as basics of servers/internet but I have everything done in Arduino IDE code and control the robot through web browser but I'm stuck on Communication Wifi between C# and ESP866. I need some help. Thanks in advance

You can host a REST API Server in the ESP8266 with the using the ESP8266WebServer and use your usual REST Programming in C# like RestSharp or Flurl.

Vpn client in xamarin

I want to create a vpn application such as "Touch VPN" or "Hi VPN'
How to use xamarin to connect to vpn server using .open files in the background?
There are several example source codes in Java
But I never found any source code in xamarin c#
How can I use c# for that purpose?

Please see example Xamarin.Android VPN service demo: https://github.com/luqmanhussain/XamarinAndroidVPNExample
Accodring to your several examples, you can convert java to C# code as well. There are some tips when you want to do that.
https://learn.microsoft.com/en-us/xamarin/android/get-started/java-developers

It depends on which protocol you need. But if you need a custom protocol or want to develop your own protocol in .NET using Xamarin, you can see our VpnHood project, a component base VPN via NuGet packages. It is in C# and uses Xamarin to develop the client for Android.
https://github.com/vpnhood/VpnHood

UWP app and WPF app communication through local network

What is the best approach to communicate between UWP app (client app) installed on phone and WPF app itself installed on local machine if they are connected to the same router? Files should sync from client to server and vice versa.
As I investigated before there are WCF, Sockets, and Web. So what is the best one to use to create such functionality?

It does not matter if the app is WPF or UWP. To choose framework like WCF or Sockets you need to know how complex your scenario is. If it is rather simple, I would advice agains WCF. It can be unnecessary complicated for basic usage. You can try web api - lite system using JSON. Generally speaking, I do recommend the framework enabling http protocol as it is reusable for almost every scenario. But that is not filter that would help you much :D

For UWP that have not allowed calling localhost and you can use it to communicate to local wpf app.
More details here and here.
But you can make the uwp communicate to local wpf app in debug, see Deploying and debugging Universal Windows Platform (UWP) apps - UWP app developer | Microsoft Docs
If you want your uwp app can use localhost in release that you should use checknetisolation and you can see some way to use wcf in the article.

Is there any sample about using OpenFire's Plugins through Jabber.net Library in C#?

I am working on C#-WPF project about IM. after some googling I Found One of the best choices to do this is Jabber/XMPP protocol so I install OpenFire as Jabber server and write a simple client application in C# by Jabber.net library. Now I want to use Kraken IM Gateway (One Of the OpenFire's Plugin) in my client application, But How?

C# application to connect to a mobile application using bluetooth

I`m asking this question again as I got no answer for about a week now ...
I want to know how to write a C# desktop application that can connect to the mobile version of the same application (that I will create). The desktop application will be used as a backup/restore for the mobile application.
I want to know also how to write the mobile version (using C# if possible).

May i know, in what way you want to communicate with the mobile version of the application? Ideally the cross domain/application communication is possible using services(WCF/Webservices).
I hope the following link may be useful for you : Bluetooth in C#, Which stack, Which SDK?