Is it better to adapt an ordinary guitar, or to buy a ready-made three-string guitar?

Personally, I prefer to adapt small classical guitars as I find them more comfortable to play. Watch a video here on how to do the adaptation. But there are several nice good quality ready-made 3-string guitar brands if you prefer, such as the Loog and the Merlin Seagull.

What is the thought behind the G - D - G tuning?

By tuning root - fifth - octave we provide ourselves with an easy all-purpose background chord on the the open strings. We can then build any scale we like above that chord. 

The actual starting note is not so important - on a larger guitar, a lower pitch might be more appropriate.

Find more detail in this pdf

Can I try out this material using an ordinary six string guitar?

Yes, and there's a video here to show you exactly how to do that. 

What is the thinking behind the notation?

The course is really not about notation - the idea is that the pupil will learn the pieces first and foremost by ear, and the notation is only there to jog the memory.  It's a very simple form of tablature which makes it easy not only to find the notes, but to count accurately. It introduces the ideas of beats and bars without requiring the pupil to learn any musical symbols at all. 

Why is the music grouped in so many different ways?

The assumption is that every pupil or teacher will navigate through the materials in a different way. Once you have selected a piece to learn, sometimes it is useful to have an overview of all the other pieces which are at the same technical level. At other times it is more useful to quickly see the other parts of the same piece, to enable duet playing or group playing.