Does the caregiver with power of attorney have the right to draw out money from the person he's caring for for his or her personal use?

In theory a DPOA has a required fiduciary duty to do things for the benefit of the individual or the assets they own. A DPOA is not supposed to do any “self dealing”..... like transfer a home to their name or close put a bank account and move all the $ into an account in their (the DPOAs) name.

James if you still mow the lawn (what r u doing next spring?) and went online to do this post, well, imho your totally competent and cognitive and you don’t need your DPOA to be micromanaging your finances. I’m guessing you’d like to keep all nice with the DPOA? If so, Maybe what you can do is require 2 signatures on all checks over a set amount (maybe $100?) and then limit any access by the Dpoa to a debit card attached to your one of your bank accouns. You go to the bank to do this on your own; personally I’d remove any signatory ability on all accounts but a single checking account for the DPOA as well.
If you move to online payment for everything (utilities, insurance, etc) house, that stops a lot of the .... but but I need a debit card... nonsense.

Out of curiosity, is the Dpoa a friend rather than family?

No, they cannot. If you wish to change POA, given you are mentally capable of understanding what you are doing, you can do that at any time. Your caregiver may leave at that time, so not something to take lightly. Is this POA on your bank accounts as your POA now, and paying your bills. Is he or she supplying you with monthly statements of your assets and expenditures? You may want to see a Lawyer. Some are now making house calls. You can feel free to call APS also, and explain your view of things, as for a case to be opened to explore expenditures and payments, etc.

They probably don't have the right for their own personal use.
As whether or not the bank will allow them, not sure.
POA is effective when you can't do things yourself.
Others here know more about this.