First of all, strictly speaking, it's not possible to have a real-time Web service. Please see:
http://en.wikipedia.org/wiki/Real-time_computing[
^].
And this is impossible due to the nature of Internet hardware and protocols. Real-time networks do exist, but they are based on different protocols and even different hardware. Perhaps you meant something else and just used a long term. If you explain exactly what did you mean by "real time", we could discuss it.
And it's not clear what help you may need. You just need to keep doing what you are already doing: conduct your research until all of the stuff gets "organized in your head".
Some separate points though:
First of all, you are talking about
streaming technologies, so you may need to start here:
http://en.wikipedia.org/wiki/Streaming_media[
^].
Now, about multiple client-side platforms? Is it really so? Yes and no. If you are determined to use only C#, the platform has to be only one, just the same: CLR:
http://en.wikipedia.org/wiki/Common_Language_Runtime[
^].
The only problem is: on what mobile platforms can you use it? Yes, you can have SLR implementation in quite a few of them. Most, if not all implementations, except Microsofts, are based on Mono:
http://en.wikipedia.org/wiki/Mono_%28software%29[
^],
http://www.mono-project.com/[
^].
On "desktop" platforms, this open-source CLR implementation comes free of charge. Not exactly so for mobile platforms. Please see:
http://en.wikipedia.org/wiki/Xamarin[
^],
http://www.xamarin.com/[
^].
In addition to desktop Linux and Mac OS X, which you can cover free of charge, you can have CLR on Androis, iOS and more. Combined with Microsoft Mobile platform, it can give you a pretty good platform coverage, all just with CLR C# programming. Do your research.
—SA