It is possible to call native code from Unity (e.g. on iOS), but it might be slow.
http://docs.unity3d.com/Documentation/Manual/PluginsForIOS.html
http://docs.unity3d.com/Documentation/Manual/Plugins.html
Unity is currently using a version of Mono at something equivalent to .NET 3.5.
Here’s a list of Unity tutorials: http://answers.unity3d.com/questions/12321/how-can-i-start-learning-unity-fast-list-of-tutori.html
Here’s another one: http://www.burgzergarcade.com/hack-slash-rpg-unity3d-game-engine-tutorial
And here’s more: http://catlikecoding.com/unity/tutorials/
Unity networking: http://docs.unity3d.com/Documentation/Components/NetworkReferenceGuide.html and http://docs.unity3d.com/Documentation/Manual/NetworkedMultiplayer.html
Here’s a blog aggregator about Mono: http://go-mono.com/monologue/
This is the main Mono page: http://www.mono-project.com
Wikipedia on Mono: http://en.wikipedia.org/wiki/Mono_(software)
Xamarin is now the Mono developer: http://xamarin.com/
Care with marshalling in Unity/Mono and iOS: http://www.snowbolt.com/index.php/blog/28-tech/91-pinvoke
WiTap, socket example on iOS: http://developer.apple.com/library/ios/#samplecode/WiTap/Introduction/Intro.html
Network stream programming on Cocoa: http://developer.apple.com/library/mac/#documentation/Cocoa/Conceptual/Streams/Streams.html#//apple_ref/doc/uid/10000188-SW1