My mother passed away last week. My step-father is the executor of the will and I am the executor if he dies. He is in the assisted living facility and has some dementia. I'm his power of attorney. Does this give the right to take over the executor job for him? What if is niece takes over the POA? Does she have the rights for him? This is hard for me if she does because this is my mother and the niece is no blood relation.

Also, do all wills need to go through probate court? Since everything was jointly owned and my stepfather gets it all, is it a simple case of taking my mother's name off everything?

Yes, if you named the successor executor, then his incapacity allows you to take over.

What about debts? If everything was held jointly with right of survivorship, then the assets pass to the stepfather outside the estate and all that is necessary is to change the ownership.

Therefore, if the niece gets poa for him, I still take over on my mother's will?

Yes, her having a POA doesn't change the terms of your mother's will. If the will didn't name a successor executor, then she might be able to argue the point. She can still argue, but that would mean hashing it out in probate court and I don't think she will win.

If you already have a POA, he would need to give her one, and if he is not competent, then he can't assign a new POA.