Legal Question in Wills and Trusts in Massachusetts

No. It means you have access to those accounts only.

No, a power of attorney is a document that allows you to make certain legal decisions for the elder. This document would need to be drafted and spell out specific powers you would be entitled.

If you are added as joint holders on her bank account, you are entitled only to the rights associated as an account holder.

I agree with the previous attorney. Your mother probably wants to allow you access during her life, and make sure that you have immediate access to those funds upon her death. If your mother is concerned about losing capacity at some point, I would strongly urge her to consider retaining counsel to prepare a Power of Attorney, and perhaps some other essential estate planning instruments.