No - you would only need POA if there are signs that your mother is likely to develop sufficient incapacity that she needed you to act for her - signs of dementia for example.
If she is of sound mind, then there is no reason why she can't give you money if she wishes.
You do not need a PoA - in fact it is better if you do NOT have one under these circumstances. But for a gift of this magnitude, if it is a significant part of her wealth, it is a really good idea if your mother takes legal advice in case it is later challenged that she did not have capacity or this was a result of undue influence. This really depends on whether she has left a Will and to whom she has bequeathed her estate.
No. If she wants to draw one up to be brought in use at some time in the future, should it become necessary, she can. It is completely up to her. Her decision alone.