Can one use terrestrial thermodynamics, which is known to apply to bounded and isolated bodies, for the whole universe? If so, is the universe bounded and from what is the universe isolated?

No, we cannot use terrestrial thermodynamics to whole universe.
Thermodynamic system is a finite region of space which we select for experimentation. The region may contain some quantity of matter and may have a real or imaginary boundary. The boundary can be fixed or movable. The energy and matter may or may not cross the boundary. The region of universe beyond the boundary is called surroundings or environment.
Whole universe is endless. We do not have any idea about the limit of the universe beyond our observation. We see all observable things in the universe. We don’t know, the universe is a bounded body or isolated body. That is why we cannot use terrestrial thermodynamics to the whole universe.