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Communication between C# and C++ application

I have just start learning about WCF that can help me for the communication between two different platform application. I have also created one simple application for the communication but both client and service are written in C#. I want to know how I can establish a C++ and C# application so that they communicate to each other. Thanks in advance

this question seems very wide to me, the thing is since you are in windows, and the C# and C++ applicattions will be running simultaneously, you have to thing in the specific requeriments of you appliccation.
For example, I had a Server in C# wich recived some data, that had to be processed in C++ and then returned to the sender, so, since the C# and C++ process were in the same computer I used a File Mapping method, for example.
Indepently of the language, what you have to make sure, is that the data you send, wen you recive it in the other process, that should be able to be understood.
Here is a link for more info in wnidows
https://msdn.microsoft.com/en-us/library/windows/desktop/aa365574(v=vs.85).aspx

How to communicate between two C# applications(sending messages and receiving messages)?

As per my knowledge, I knew that messages can posted from one application to other application using "SendMessage" or "PostMessage".
I tried using SignalR to communicate b/w the applications. The problem here i found was server should be launched as a console application and clients will be my winforms. Ideally I don't want to show this console application as it seems to be weird for the user. If there is any work around for this approach please suggest.
After signalR I came across EventAggregrator in c#. Can we use EventAggregrator to communicate b/w two different C# applications? If yes could some one give an example on how to do this.

Until a few years ago, Socket class was the right way to do this. There are probably more modern, robust and easier ways to achieve the same result nowadays, but you may want to look at what's under the hood.
Socket class on MSDN:
https://msdn.microsoft.com/it-it/library/system.net.sockets.socket%28v=vs.110%29.aspx?f=255&MSPPError=-2147217396
Client-server example on CodeProject:
https://www.codeproject.com/articles/463947/working-with-sockets-in-csharp

Communication between a C# and Python application hosted on the same machine

We're working on a project that requires us to interface with a specific set of hardware; one set can be controlled very easily using C#, the other of which is natively programmed using Python. Part of the project involves getting the hardware running on Python to communicate with the hardware running through C#, and unfortunately, due to time constraints, we aren't able to create a set of C# or Python software to control the other set of hardware.
The set of hardware running on Python is completely event based, in that we can program functions that are called when certain conditions are met by the hardware. Our thought was to modify the C# application controlling the other set of hardware to host the Python application (using something like Application.Run()), then program the Python functions to propagate relevant data to the C# application as the events come in from the hardware.
We're considering using a socket connection to handle communication between the two, as both C# and Python are fairly simple to get working that way (or so our Python guy claims). The biggest concern with this that we have is if there will be any issues with the fact that both programs will be hosted on the same machine. If this won't be an issue, we would probably end up using a shared library such as 0MQ
We've also done some research into the following areas:
Pipes / Named Pipes
Message Queues
Shared Memory
Basically we want to know which method of these (or any others) will be the easiest to implement with these languages, and which will give us the best performance. We are concerned only with speed and accuracy of the data (ie, if using network packets, one that will drop the least). Security is not a concern.
Ideally, there should be one data stream going from the Python application to the C# application, and two data streams going from the the C# application to the Python application. The host machine will be running Windows 7. I can give additional information as needed.

One option is to try IronPython. Since IronPython is a .NET language, communicating with C# code should be easy.
It seems worth looking into how hard it would be to get your existing Python code running on IronPython.

Interprocess Communication Between C# application and unmanaged C++ application

I have two Windows services, the first one written in C# and the second written in
unmanaged C++, I want to know how can I do two-way interprocess communication.

If the interprocess communication is always going to be done on the same machine, named pipes is the way to go because they are faster than other options.
However, if there is even the slightest chance that this communication might occur across machine boundaries at some point, go with the socket approach. For C++, you'll need the winsock2.h header file. In C#, use the System.Net.Sockets namespace.
It's been a while since I've done unmanaged C++, but my recollection is that you'll have to write less C++ code if you create the server on the C++ side and then use the TcpClient class on the C# side.

Sockets are probably your best bet.
With sockets your not necessarily tied to both programs being on the same machine.
Also, it's likely to be the most portable option (heck, Windows even has select() for sockets).

Sockets and Named Pipes are two options well supported in the managed and unmanaged environments.

There are a number of ways to do this, but I think that the best way would be to use WCF and COM+. If you host a service in COM+, you can access it through WCF in your .NET service, and through COM interfaces in your unmanaged code.
You might want to check out the following sections of the MSDN documentation to get started:
Integrating WCF Services with COM+:
http://msdn.microsoft.com/en-us/library/bb735856.aspx
Integrating with COM+ Applications Overview:
http://msdn.microsoft.com/en-us/library/ms734723.aspx

I would say sockets and a messaging system. Check our for Google Protocol Buffers.

Use either DCOM/RPC or named pipes - anything else is either insecure, hacky, or both.

Create a Singleton COM object. Maintain data in this COM object, which can be read by both C++ and C# applications.

I would say redis would be the best solution for any kind of interprocess communication

What is the best way to pass information from a C# app to a C++ app while both are running?

What would be the best way to pass information from a windows forms C# app to a MFC C++ app while they are running? I don't need to send much, just a small string.
Thanks,
Jeff

Going down the list of IPC options:
Memory mapped files. Easy in C++, tough in C# without pointers, awkward handshaking
WM_COPYDATA. Easy in both, tricky to find the window handle you'll need
Clipboard. Easy in both, very awkward handshaking
COM. Out-of-proc is a beast, forget about it
Mailslots. Not suitable for one-to-one communication
Pipes. Easy in .NET 3.5, do-able in C++ but a bit tricky to get right
Sockets. Easy in both, hard to pass up.

Use named pipes, see this posting.

If the C++ app has a main window, take a look at using the SendMessage function (via P/Invoke) in the C# app to send a WM_COPYDATA message to the C++ app.
http://msdn.microsoft.com/en-us/library/ms649011%28VS.85%29.aspx

MailSlot api is small and simple but requires P/Invoke to use from c# and can go outside your local machine so needs care.
see my answer here
Named pipes may well be more robust but this is an alternate.