Questions regarding Power-of-Attorney, after individual deemed to lack decisional capacity, vs. Guardianship.

Hello, 1) If a family members is designated under a trust to serve as Financial and Health Power-of-Attorney under a previously established trust, does that individual become a legal Guardian after their loved one is cognitive compromised, say for example due to dementia? To my understanding, "competence," is a legal term/facet that is determined by a Court Judge, not a physician. Health professionals can only provide a medical opinion if a individual has "decisional capacity," which is different than competency. 2) Should a person become incapacitated, due to onset of Alzheimer's type dementia or sequalae of CVA, are they able to revoke POA? To my understanding, they are able to do so if there is a "moment of lucidity." The problem exists, however, as a moment of lucidity is just that - transient and often fleeting. Even if this brief clarity does exist, they may not be able to process/synthesize the magnitude of their situation, as they were of unclear mind when being told of their health condition. As an example, person wants to designated his brother as POA, as he no longer wishes to live in a nursing home environment and the brother supports him to leave, despite the person having marked physical ailments (hemiparesis/hemiplegia) that would interfere with safety in a non-skilled environment. 3) As a person must show impairment with "instrumental functions" in activities of daily living, such as handling finances, managing medications, cleaning house, etc. for a diagnosis of dementia to be made, would physical constraints that preclude these activities from being performed independently, due to say a CVA, constitute a deficit with independently executing instrumental/functional ADL's? If physically unable, but cognitively considerably adequate, can a diagnosis of dementia still be made?