We present a first-principles study of the atomic, electronic, and magnetic properties of two-dimensional 2D, single and bilayer ZnO in honeycomb structure and its armchair and zigzag nanoribbons. In order to reveal the dimensionality effects, our study includes also bulk ZnO in wurtzite, zincblende, and hexagonal structures. The stability of 2D ZnO, its nanoribbons and flakes are analyzed by phonon frequency, as well as by finite temperature ab initio molecular-dynamics calculations. 2D ZnO in honeycomb structure and its armchair nanoribbons are nonmagnetic semiconductors but acquire net magnetic moment upon the creation of zinc-vacancy defect. Zigzag ZnO nanoribbons are ferromagnetic metals with spins localized at the oxygen atoms at the edges and have high spin polarization at the Fermi level. However, they change to nonmagnetic metal upon termination of their edges with hydrogen atoms. From the phonon calculations, the fourth acoustical mode specified as twisting mode is also revealed for armchair nanoribbon. Under tensile stress the nanoribbons are deformed elastically maintaining honeycomblike structure but yield at high strains. Beyond yielding point honeycomblike structure undergo a structural change and deform plastically by forming large polygons. The variation in the electronic and magnetic properties of these nanoribbons have been examined under strain. It appears that plastically deformed nanoribbons may offer a new class of materials with diverse properties.