Is it legal for a person who is not related to an incapacitated person to be his power of attorney and do you have to be a legal resident to be one?

There is no requirement that an agent be related to the principal. The issue is whether the grant of power was knowing and willing, and made at a time when the principal had capacity to know and understand the effect of issuing the power. Also, unless the power is "durable," it does not survive a subsequent incapacity under California law.

Anyone can hold a power of attorney. The second question depends on the terms of the POA.

Any one can be given a power of attorney but they can only act for the benefit of the person granting the power and only to do those things listed in the power when the grantor is unable to do them. They can not do something that is really just for their benefit.

Yes, an attorney-in-fact (that's the name for a person who is given authority by a power of attorney) can be someone who is not related. Yes, the attorney-in-fact can be someone who is not a legal resident. Yes, the attorney-in-fact probably could enter the home, but only if they are doing so for the benefit of the incapacitated person. No, the attorney-in-fact absolutely cannot claim the incapacitated person's belongings as their own, because they must only use the power of attorney for the benefit of the incapacitated person.