This is one of my very rare posts and I'm not sure it's of any benefit. When my late wife use to see people that I could not or I found her talking to herself, I didn't find it a big deal. I just went along with it. Once she was unhappy with 'someone' sitting opposite her. Politely asked the 'person' to move and sat in 'his' chair.
As for talking to ones self, some children do it. I can relate to that, as it was a form of escapism to a safer place.
Once my wife found me chatting away while I worked on our land. When she questioned me I replied: "I'm only thinking out loud". "But you were arguing with yourself". "So what, it's time to take me away when I lose the arguments."
The point I'm making is, do your best to enter their world. That world may well be of a time or place you know little of. During and after the war there was rationing We did not have fridges or freezers, just a pantry to place perishable goods. Your Mums, Dads and Grandparents lived in another world they knew and felt safe with. Remember the mind of an AD patient is not unlike a box of tissues 'the first tissue in, is the last to leave'.
A journey back in time to their world can be very edifying in helping to understand what you perceive as strange.
Maybe I was just fortunate in being such an oddball, by caring for my wife all the way on my own 24/7 in my own way. I don't give advice nor take it for that matter, just relate my experiences with a system I found stressful and frustrating. As a result I opted out and followed my own path. Sorry it's so long winded. It's OK for each to do their own thing or follow the standard path strewn with more questions than answers.