No, they are not. They can be caused by Alzheimer's disease as a consequence, but not vice versa. Well, they can be caused due to the fact that with Alzheimer's brain cells (memory cells) suffer, and a person simply forgets not only events, but also part of himself. More precisely, he remembers what was long ago (short-term memory deteriorates at the initial stage). In view of this, a person, looking at himself in the mirror, may simply not recognize himself and not accept the fact that it is him. My great-grandmother was 86 with Alzheimer's. And once, looking at herself in the mirror, she asked: "Who is this?" I answered her: "Granny, it's you." "What nonsense are you talking about? How old do you think I am?" "You are 86." "No! I'm 60!" Something like that.
Derealization and depersonalization are different things, after all.
The first is a violation of the perception of reality, characterized by the emergence of a feeling of unreality of what is happening, the loss of the "brilliance" of the surrounding world.
Depersonalization is a violation of self-perception, the emergence of a feeling of "third-person view", a look from the outside at their actions, the inability to control them and what is happening in general.
Indeed, they often exist in conjunction.
And now about whether these are precisely the harbingers of alzheimer's, dementia, or symptoms that indicate a predisposition to them.
No, it is not. Derealization and depersonalization can manifest in different situations. For example, a prolonged stay in a stressful state can cause such sensations.
Of course, there is always the possibility that these are symptoms of more serious mental problems, so it is worth contacting a psychologist, especially if the problem causes concern.