I'm writing a universal app by using windows 10, visual studio 2015 and C#. I would like to run this app on windows, Linux and mac. I know mono doesn't implements windows presentation framework, so, if I write a WPF app it runs onluy on windows. Now, if I write a universal app, can mono run that? If yes, how?
The holy grail .Net UI question :-)
TL;DR Answer = No.
Universal Windows Platform (UWP) core APIs (also known as Windows Runtime / WinRT) and the resulting APPX based applications only target Windows 10 platforms (Phone, PC, Tablet...) as those APIs and runtime do not exist on the other desktops.
Using Xamarin/Mono you could reuse a portion of the C# app's 'business' level logic but the presentation layer and GUI logic would have to be re-written using a different GUI (Native Widgets, GTK#, QTSharp, HTML/CSS/NodeJs, etc...). Same model that people have been using Xamarin for C# based mobile development applies, share your C# app logic across platforms and use Xamarin.Mac to build a native OS-X UI, and/or build a UI using GTK#, embed your app's runtime logic into a Electron/Blink shell, etc..
Currently the Windows 10 for Apache Cordova project which is HTML, JavaScript, and CSS, only targets Mobile (WinPhone, iOS, Android) and Windows 10 PC/Tablet platforms. That is not to say someone could not develop a new Cordova target to include OS-X and Linux desktop manager support (but I do not know of any that have not already stalled) :-/
Even Microsoft's xplat-based Visual Studio Code for Linux and OS-X uses Electron (Chromium based) to deploy the io.js based application along with the Blink layout engine to render the UI, all done in HTML/CSS/JS.