1. Group is a term for a node in the data source tree structure that can contain other elements. A section is a form control that is bound to a node in your data source and serves to determine the context of controls inside of it. Sections can also be conditionally hidden or colored based on changing conditions. Sections are most often bound to groups, but they can be bound to any type of node.
2. I don't believe there's a way to relocate a whole bunch of nodes at once. You can move them to a new location one at a time by right-clicking them in the data source taskpane and selecting Move....
3. Layout tables are purely for layout and presentation and have no bearing on the data in your form.