Gillie,
Regarding rod plane, yes, your understanding is correct. I tend to keep my rod at a lower angle thoughout the sweep and D loop formation.
Keeping the sweep closer to the water is not very important at all. It is just something I prefer to do a lot of the time. You can cast long belly lines with the rod parallel to the water or with the rod at a much higher angle. The important thing is keeping the rod motion pretty much on the same plane as make your sweep and form the D loop, and this is the same whether using a short belly or a long belly. You just need to apply more power to the long belly sweep and D loop formation because you are aerializing more line.
It is pretty much underhand casting. Keep in mind that underhand casting is only one way to do it. You can also use the bottom hand more or less as a fulcrum and use the top hand to apply power to the cast. Or you can use both hands in concert to apply power to the cast by pulling with the bottom while pushing with the top. All of these work, and one is not superior to the others, they are just different.
The high stop is important in order to keep the line aerialized above the water on the final forward delivery (or forward spey) regardless of angle of the rod on sweep and D loop formation or whether casting with power being applied underhand, top hand, or both hands. If the stop is not high enough, the line will either roll out along the water and not above it, or slap the water and not go very far.