Is the POA responsible for making sure my mom with dementia has food, is taken to doctors and is generally looked after?

If your Mom has been found incompetent to handle her own affairs then yes I think the POA has some responsibility here. No, they don't have to be hands on but they are responsible for making sure the person is cared for. They should be personally or hiring (with Moms money) someone to check on her and arranging to have her taken to appts. Her bills should be being paid. The POA is entitled to no payment for services unless written in the POA.

If you find that the POA is nor carrying out their duties or taking money they aren't entitled to, then contact the lawyer who wrote up the POA. The only other thing u can do is get guardianship that overrides POAs. This is expensive but u may be able to use Moms money if you win. You may want to consult with a lawyer.

Depends on if your mom has capacity or not. POA's are for decision making, not necessarily doing errands and taking her doctor appointments.

POA is responsible for lining up the help that is needed not providing that help themselves.