I don't know how or why I know this, but I don't believe that she can. Oddly enough, succession is defined in British law, and it's not left to the Queen to place the heirs in order. That is predetermined by birth. If William is to become king, either Charles must die or abdicate.
Again, I'm no authority, so I could be wrong.
You are correct.
There’s a bunch of laws on succession but the most important is the Act of Settlement of 1701. The Queen can not alter these laws as they are Acts of Parliament - Parliament can alter them.