Hi Mati!

Let's answer these questions...

1) both will create a bone. When you do it with the create tool you conveniently create the bone where you click. When you do it through the New>Bone menu the bone is placed at the tip of the parent bone and it can be useful to create IK targets so that your contrained bones don't move trying to follow the target bone. (you'll need to reparent the created bone so that it's not a child of the constrained ones, but that's the main perk IMHO)

2) Skin bones and constraints are actually a new feature of skins. As you expected, they in fact used to contain anything that can go in a slot (such as an attachment, a mesh, or a point attachment for example) under a skin placeholder. When you create a skin and select it, if you place something inside a skin placeholder, this will only be visible and active when the skin is active. You can read more on these user guide pages:
Skins - Spine User Guide
Skins view - Spine User Guide

Do you also need clarifications on the terms you wrote in the title?

The root is a bone that is the origin of your skeletons. Anything else is a child of this bone and you can't delete it.
Everything else is conveniently on this page: Basic Concepts - Spine User Guide