Bob, your question about how much activity your dad can safely do and if assisted walking is causing syncopated episodes is something you should ask your dad’s doctor about.

It’s not uncommon for people who are chair/bed bound with dementia to not eat or drink very much. For most of us, caregiving is intertwined with nurturing with food.

You might find these nutrition questions and answers helpful:
https://www.virtualhospice.ca/en_US/Main+Site+Navigation/Home/Support/Support/Asked+and+Answered/Nutrition.aspx
How is your dad doing? Is he home or in the hospital?