With my medical power of attorney, I have hired my niece to live for free with my mom and care for her 24/7. Can the person with my mom's power of attorney just have my mom gift her granddaughter a salary of $3,500 per month or do we have to pay social security and unemployement on it.

Ok, first I would check and see if the medical POA would cover a care giver, I would prefer to see this beig a more general power of attorney, since this includes rental of home ( in exchange for work) and now getting into payment of taxes and more.

Several things, first the value of the rental is "pay" and that value should be recorded on a 1099 as pay to the person who would have to pay taxes on the value of the rental.

next no this is not a tax, it is a salary, and social security taxes, income taxes have to be paid.

you are the employor has to pay matching social security funds ( ot held out of check but you have to pay) and you also have to pay unemployment.

Also you need to check state law about the requirement for having them covered under workers comp insurance.
** what if they hurt their back lifting mom and sues you and mom for 10's of thousands of dollars.

next a POA is not a guardian and can only sign for the other person if they are not available. So mom should be signing or givng the OK o all of this since she is available,

Even if she is a relative, giving her room and board for 24/7 care creates an employee/employer relationship. If she lived there but had an outside job that would be different.