Do hemineglect, hemiplegia occur from damage to the parietal lobe?

Yes: Contralateral weakness can be present. Sensation is altered on the same side, and pts have trouble localizing motion in time and space. Extinction phenomena occur, position sensation can be lost, the affected limb may not be recognized or even thought to be part of another person.

Anosognosia, or denial of a deficit, is not limited to those with hemiparesis/plegia (yes, typically these are right hemisphere with parietal lobe structural damage). Deficits in awareness involving judgement, emotions, memory, executive functioning, and language skills as well (with correlation to respective brain areas involved) can be found in stroke, dementia, mental illness and more.