We studied, by scanning tunneling microscopy, the morphology of nanopits of monolayer depth created at graphite surfaces by hydrogen plasma etching under various conditions such as H$_2$ pressure, temperature, etching time, and RF power of the plasma generation. In addition to the known pressure-induced transition of the nanopit morphology, we found a sharp temperature-induced transition from many small rather round nanopits of ~150 nm size to few large hexagonal ones of 300-600 nm within a narrow temperature range. The remote and direct plasma modes switching mechanism, which was proposed to explain the pressure-induced transition, is not directly applicable to this newly found transition. Scanning tunneling spectroscopy (STS) measurements of edges of the hexagonal nanopits fabricated at graphite surfaces by this method show clear signatures of the peculiar electronic state localized at the zigzag edge (edge state), i.e., a prominent peak near the Fermi energy accompanied by suppressions on either side in the local density of states. These observations indicate that the hexagonal nanopits consist of a high density of zigzag edges. The STS data also revealed a domain structure of the edge state in which the electronic state varies over a length scale of ~3 nm along the edge. The present study will pave the way for microscopic understanding of the anisotropic etching mechanism and of spin polarization in zigzag nanoribbons which are promising key elements for future graphene nanoelectronics.