You will need to check with your state law. Generally, the tax return for a deceased person can only be filed by that person's legal representative. If the deceased was married, the spouse would automatically be allowed, but if the deceased was not married, then someone has to follow your state law to appoint a representative. In the case of a person with a small or no estate, and no disagreement among the surviving relatives, it may be a simple form that you fax to the county clerk's office or the clerk of the probate court. Look on your state's government web site for information about small estates.
Only the person that has control over the mother's estate, who has power to do so;but you will need to speak with an attorney.
Mom doesn't have an Estate as she hasn't died. She's in a nursing home and is incoherent. Under those circumstances, a Durable Power of Attorney holder can act for her.
Except the deceased is the taxpayer's brother. The mother *might* automatically be the designated representative under the laws of this particular state, but might not. Check your state laws on probate of small estates.