Can someone with Power of Attorney open a person's will while they are still alive and act on it?
Can they do so without involving the executor of the will?

By "act on it" do you mean change it?

And also, what do you mean "open" it? Is it in a sealed envelope? Who has possession of it?

If you mean is the person with the POA allowed to examine and read the will, yes, if that person has access to it. But the will has no legal effect until the testator dies, so it would not really serve any conceivable purpose to do so.

No one can act on a will until the testator is deceased. At that point it has to be submitted to probate so an executor can be assigned. As soon as the grantor of a POA dies, the POA becomes invalid.

Only the testator can modify a will. A POA does not give someone the right to make changes.

A POA is a person who can sign for the other person, They can not make choices and changes for that person. It is still the other persons choices