If she can just make an X, a notary can validate the signature. I am a Notary. But, I question crossing the border or getting on an airplane with a dementia patient. It could get messy.
An escrow account is where part of your mother's monthly payments for her house goes to in order to pay other bills like property tax and home owners insurance. A mortgage company is not going to let you take money from that account because you have guardianship.
How much longer does your mom have to pay for the house?
A POA or Guardianship will not help your mother renew her US passport. Why does she need a US passport.
An escrow account is where part of your mother's monthly payments for her house goes to in order to pay other bills like property tax and home owners insurance. A mortgage company is not going to let you take money from that account because you have guardianship.
How much longer does your mom have to pay for the house?