Yes. Cognitive function can be measured in various facets, eg executive function, praxia, phasia, gnosia & memory. If you can't remember things, it's very difficult to receive information enough to learn. This is one of the basic tenets of cognitive impairment.
Yes. It's really more complex than this, since there are many steps between stimulus, initial neurological firing, and conscious perception. All faculties have to be intact or messages from the environment don't get through without distortion. There can be processing problems with information once it gets in, even if it the initial sense organs receiving it are intact. Misinterpretations result.
Absolutely. Cognitive impairment means that parts of persons cognitive or thinking processes are impaired. This can also include perceptual disturbances or misinterpretations pertaining to information coming from the environment as well as information originating inside the persons mind.
Mirror, mirror. Yes. Lack of recognition can be for different aspects such as facial, recognition of vocal quality, or unawareness of relationships of one person to the other. Yet lack of recognition is not a universal symptom of cognitive impairment.
Maybe. Not all faculties need be involved in each case of cognitive impairment. Reduced communication certainly is common in such cases but can also be seen during anger or other strong emotional states.