Piece of cake:
- an API is an interface. It's like the specification of the telephone system or the electrical wiring in your house. Anything* can use it as long as it knows how to interface. You can even buy off-the-shelf software to use a particular API, just as you can buy off the shelf telephone equipment or devices that plug into the AC wiring in your house.
- an SDK is implementation tooling. It's like a kit that allows** you to build something custom to hook up to the telephone system or electrical wiring.
*Anything can use an API. Some APIs have security provisions to require license keys, authentication, etc. which may prohibit complete use of the API in particular instances, but that's only because particular authentication/authorization steps fail. Any software that presents the right credentials (if required) can use the API.
**Technically, if an API is well-documented, you don't need an SDK to build your own software to use the API. But having an SDK generally makes the process much easier.
A) With the Windows Mobile 6.0 SDK, you can target Windows Mobile devices obviously, there are two main categories: Windows Mobile Professional (Formerly known as Pocket PC) and Windows Mobile Standard (Formerly know as Smartphone). The main difference is that Professional supports touch screens and standard does not, but you can run the same binary on both and the distinction is going away in the future.
C) (you skipped b) if you are using the Windows Mobile SDK, you need a windows mobile device like the T-Mobile Wing (Professional) or the T-Mobile Dash (Standard)
D) all Windows Mobile devices are advertised as such, if the device says it runs Windows Mobile you will be ok.
e) No, you can also develop for Symbian (Nokia & Sony Erickson), Backberry, iPhone and Android among others. iPhone and Android are very popular at the moment, if you are just starting I would suggest Android, you can get the T-Mobile G1 or the Google ADP1 (same hardware) and the development tools are free (eclipse + Java SDK + Android SDK).
Update:
To clarify on e)
You need different tools/devices for each platform you are targeting, for example:
1) For Windows Mobile you need a Windows Mobile Device (i.e. T-Mobile Dash or T-Mobile Wing), a Windows Desktop and Visual Studio.
2) For Android you need an Android Device (i.e. T-Mobile G1 or Google ADP1), one of the following desktops (Windows, Linux or Mac), Eclipse (a free download) and the Android SDK (another free download).
3) For iPhone you need an iPhone and Mac desktop, you can download the SDK from Apples web site.
Symbian and blackberry would be similar, you need separate devices and tools for developing for them.
Update #2:
Most of the mentioned platforms and SDKs support some sort of emulation so that you can develop without a physical device, however I don't recommend going that route but for the simplest of applications as in my experience, the variations with real life devices are big enough as to warrant extra testing on your target device anyway.
Update #3:
One more thing, if you want to remain using C# only, then your only option is Windows Mobile as that's the only platform with support for that language. for the iPhone you will need to learn Objective C, for BlackBerry and Android you need Java, and for Symbian you can do C++ and Java.
Best Answer
There is Khronos OpenGL ES 2.0 SDK for Imagination POWERVR chips (SGX). It can be used to develop OpenGL ES 2.0 applications on PC. That's pretty handy. If you are targeting to some non-POWERVR chip, you can still use the SDK, but I have no idea if it helps at all when making actual Windows Mobile-build.