A: If the power of attorney is broad enough, he can do anything your mother could do. He is restricted by the terms of the power. Unless there is language or agreement that prevents it, your mother could sell her one-half interest in the house, just as you could sell your1/2 interest. He could not sell your interest unless there is some agreement giving your mother that right. Most buyers are reluctant to buy a 1/2 interest in a house. He could file a partition action, which could force the sale of the house. You should consult with an attorney to be advised of your best course of action.
A: You cannot tell if you own any mineral rights without checking the entire title chain. However, the reservation in the deed may let you know that you do not own any mineral rights. For instance, if the deed says "All mineral rights are reserved to the grantor."