Different Flavours of Windows Mobile 6

1. What are the various Windows Mobile 6.0 editions available?

Standard - Mobile 6.0 with no touch screen.
Classic - Mobile 6.0 with touch screen without phone capabalities.
Professional - Mobile 6.0 fully loaded.

2. If I intend to do some .NET development on Windows Mobile 6.0, which editions should I get?

What's New for Developers in Windows Mobile 6?
http://msdn2.microsoft.com/en-us/library/bb278115.aspx

In fact, you don't even need to get any editions. You can just download the sdk's which comes with emulators so you can test on all editions.
http://www.microsoft.com/downloads/details.aspx?familyid=06111a3a-a651-4745-88ef-3d48091a390b&displaylang=en

3. What are the differences between the various editions in terms of functionalities and limitations / restrictions when it comes to .NET development?

No major differences.

4. Do they all have got .NET Compact framework installed by default? What about SQL Mobile?

Windows Mobile 6.0 comes with .NET Compact Framework 2.0 and SQL CE 2.0.