No, signing on as your mother’s medical surrogate does not make you financially responsible for her cost of care. If and when you sign her admission agreement, simply add after your name “as personal representative and not as guarantor.”
You could have an attorney review the documents, but the reality is that they’re not negotiable. The attorney could, however, explain what they mean and answer any questions you may have. An elder law attorney can also be important if you might be applying for Medicaid on your mother’s behalf.