Archaebacteria, single-celled prokaryotes, lack nuclei and interior membranes, and exhibit diverse shapes while thriving in extreme environments due to unique cell wall and membrane structures. They reproduce asexually through methods like binary fission and play significant roles in ecological systems and biotechnological applications, such as biogas production. These organisms can be autotrophic or heterotrophic, acquiring nutrients from a variety of sources, including chemicals and decaying matter.