1. Can I handle affairs of my mother/father with their Power of Attorney, if they become unable to handle their own affairs.
With the proper provisions in a Power of Attorney, the person with the power can act for the person who gave them the power after that person becomes unable to act for themself. This can be an alternative to having to seek to be appointed guardian for that person.
2. If I have Power of Attorney for my mother/father, can I use it to handle their affairs after they die?
No. A Power of Attorney ends with the death of the person giving the power. To handle the estate of that person, you will need to be appointed personal representative or administrator of the estate.