Yes. Yes. No. No.
Maximum number of devices is hard to judge since there isn't a single definitive answer, and maximising devices by targeting older API means the app will not make use of newer features: Windows Phone Runtime apps are easy to port to Windows via Universal projects, but won't run on Windows Phone 8 devices. Windows Phone 8.0 apps will run on Windows Phone 8 devices but will be difficult to build for Windows. Windows Phone 7 apps miss many new features such as higher screen resolutions.
Windows Phone and Windows are separate (but related) OSes. Windows tablets run the same OS as Windows desktops (this is different from Android and iOS where Phone and Tablet share the OS). Windows RT runs a limited version of the desktop Windows OS.
Windows Phone apps do not run on Windows.
Windows apps do not run on Windows Phone.
Windows Universal apps bridge the two and allow essentially the same source code to be built for either Windows or Windows Phone.
Windows Phone apps are upwards compatible:
Windows Phone 7 apps run on Windows Phone 8 and 8.1. Windows Phone 8.0 apps run on Windows Phone 8.1.
Windows apps are upwards compatible:
Windows 8 Store apps will run on Windows 8 and Windows 8.1
Windows 7 desktop apps will run on Windows 8 and Windows 8.1
Windows Phone 8 supports only Windows Phone Silverlight (8.0) apps.
Windows Phone 8.1 supports Windows Phone Silverlight (8.0 & 8.1) and Windows Phone Store apps.
Windows RT supports Windows Store apps (AnyCPU or arm)
Windows 8 & 8.1 support Windows Store apps and Windows desktop apps. (AnyCPU, x86, or x64)
Windows Runtime apps are apps which use the Windows Runtime. On the Windows Phone they are called Windows Phone Store apps. On Windows they are called Windows Store apps.
Universal apps are a way to share source for Windows Runtime apps across different targets (both Windows Phone Store apps and Windows Store apps). They apps need to be compiled separately and except for very simple apps generally have some differences between the two. Typically the UI is different but the underlying app logic is the shared. From a development standpoint, a Universal app solution contains a Windows Phone project for phone specific code, a Windows project for Windows specific code, and a Shared project for shared code.
MSDN has more details at What's a Windows Runtime app?
For more on differences between Windows Phone Runtime apps and Windows Phone Silverlight apps see Migrating your Windows Phone 8 app to a Windows Runtime XAML app