The black areas are masked.
Masks are used to "protect" parts of the model from being edited by the sculpting tools. They appear as darkened areas of the mesh. The darker a masked area is, the less effect sculpting on it will have. Masks can be edited with the mask brush, as well as cleared or inverted accross the entire model. The masking feature is active as soon as sculpt mode is entered; there is no separate toggle.
Also see this: Button or menu entry to clear the sculpting mask?
The dotted red line is something different, you probably defined a render rectangle, and Ctrl-Alt-B should remove it. Also see this: Render just part of a final image from Cycles?