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What is the right way to communicate between a C# server and Windows Phone?

Ok so i have a C# server and a windows phone app that acts as a client. The client will have to modify settings on the server, receive images from the server (possibly a video stream) and receive notifications from the server (the best way would be instantaneous, like when someone sends you a message on facebook and you get the notification right away).
I have the server and client set up so they are communicating, they are sending each other an object that is serialized with XmlSerializer (it currently only contains a public String field with public get/set methods). They connect over a socket. This works well if i want to send just simple messages between them, but i assume i'll run into problems when i want to have instant notifications and transfer of images / video streams. How would i go about continuing my work in a proper way?

Consider designing an API solution via web services using RESTful or SOAP services. Personally I suggest using RESTful web services. Here are some kick start links about REST:
http://www.codeproject.com/Articles/255684/Create-and-Consume-RESTFul-Service-in-NET-Framewor
http://www.codeproject.com/Articles/148762/NET-4-0-RESTful-Web-Service-Introduction
http://www.codeproject.com/Articles/21174/Everything-About-REST-Web-Services-What-and-How-Pa
http://msdn.microsoft.com/en-us/library/dd203052.aspx
This is another useful article in MSDN which compares WCF REST and WCF SOAP: http://msdn.microsoft.com/en-us/library/vstudio/hh273094(v=vs.100).aspx

I think if you are looking for two way communication between the client and server then using sockets is the way to go.
As for images you don't need to send the actual image. You can just pass a URL to it and then download it with one of the classes specialized for that.
For near instant notifications you could also take a look at push notifications.
Of course if you don't really need the server to push data to the client then it would be much simpler if you used a REST API as someone else suggested.

Sending a data from android phone to pc?

I am creating a "tracking system" for my android phone. Basically, the phone would transmit it latitude/longitude to a C# program that will receive the coordinates and display it on a map. I managed to get the phone's latitude/longitude coordinates but I need a way to transmit that data to my C# application running in my PC. I know my way around C# and Java but never really got into network programming. Is there a way to do this ?

I'd look into C# Webservices, very powerful. The communication protocol is SOAP (Simple Object Access Protocol) which is a popular and well supported standard.
Good starting reference: Your first C# Web Service

I can't speak to the C# side of it, but if you write a C# server to receive post requests, the Apache HttpClient makes it relatively simple to send requests. There are a bunch of other questions on SO that will help with setting up the client side on your phone if you poke around a bit.

You have different way to do it.
The first is to send data over the cloud to interact through distant server. So the both devices have to be connected to Internet
The second id to send the data over a local network so the data have to be on the same network and have to share their IPs
The third is to use adb forward which allows to build a socket connection between the 2 devices over a USB cable. The requirements are that the phone have to be on debug mode I think and that the driver are installed on the PC so the phone is recognized by ADB.
I can add one more by using a Bluetooth connection. Find information here

The correct way to do it would be to build WCF service which allows many different protocols to receive data. This would could be a very powerful solution that can be extended in future.
The fastest and easiest IMO would be to create ASP.NET MVC application, define a POCO Model for your longitude/latitude and create an action that would take your Model as parameter. Then use HttpClient and HttpPost on android to send the data. The trick here is to name the variables in your post request same as ones you define in your C# Model.

Creating webplugins

I am trying to create a program that will be passed input data from events a user fires from a webpage on their browser. I am aiming at google-chrome currently with the program being in either java or C#. I know this is possible because Spotify does this, so does the Battlefield 3 PC gui. How can I go about doing this? Does the user need to install an extension or can I get that information straight from google-chrome? Note: The webpage is not being run on localhost.

You're going to want to look into web sockets. Web sockets are just cool. I got a huge grin on my face the first time I got demo working. :D
Here's a tutorial that helped me out:
http://www.developerfusion.com/article/143158/an-introduction-to-websockets/
You can create a socket listen in your appilcation then connect to it from javascript, passing whatever data you desire. It's nicer then ajax as it's a persistent open connection and you don't have the overhead of http calls.

Send Data From PHP to C# or VB.NET

Today'm trying to pass a variable and an array of PHP to a desktop application, but I have no clue how to do it.
To be more precise in my question I need PHP run the Desktop Application Developed in C # or VB.NET and send a variable.
If anyone can help me with some solution,suggestion or method is welcome Thank You.

You should send the information to the client in a format you can parse client side. XML would be one example.
So if you go the XML route (I'd look for a better transport data structure)
PHP outputs XML when the client application requests the data
The client then parses the XML pulling the data from it and storing it as a native data structure

Given your clarification in your comment (that you want to do this on the client machine), the answer is you can't. PHP doesn't run on the clients machine, it runs on your server and outputs to the clients browser, the browser then interprets that and displays the results, the browser doesn't run other applications as that is asecurity breach...except when downloading certain mime-types. If you are doing this with the users knowing cooperation, that might be a solution. If you control both code bases (the PHP and C#), then it's more likely, it would make more sense for the user to run the desktop app and for it to communicate with the PHP page to get the info it has.

C# + PHP in the same application?

What im trying to do is a little different, im wondering, if its possible to create sorts of an interface, so that if a particular function is called in php (stand alone), than the arguments will be forwarded to a method in C#, and vice versa.

Depends of course on what kind of data you want to exchange, if the applications are on the same server or on two different ones etc.
I did briding between PHP and C# in some of my web based projects. What I did: create an ASP.NET MVC project which exposes a RESTful API. The methods exposed by this API are then called from PHP via HTTP (using CURL). I used JSON as a data exchange format to pass data from PHP to C# and back again. This worked good as the two applications were on different servers.
I could also imagine some kind of socket server. E. g. a background process written in C# is listening on some port, and then you connect to it via PHP´s socket functions. I did something like this to connect PHP and Java. The Java app ran as a demon process on port XXXX and was a wrapper around Apache FOP. I used PHPs socket functions to pass XML and XSLT to the Java demon which then used Apache FOP to transform the data into a pdf and returned that via the socket connection back to PHP which in turn sent the PDF file to the client requesting the page.
There are probably some other approaches, but these were my experiences so far in connecting two different technologies together.
EDIT: as an aside: PHP on a windows webserver using IIS was really not that nice to work with. Sometimes strange errors occured or certain permission related errors that were not easy to resolve. YMMV though.