A few things...
When TB says that he will get the hat, gloves, clothes from teh Hotel.....do most Hotel rooms come equped with extra clothing items? Now some upscale ones might have a shop in the lobby, but even ordering some up to your room will bring more attention when it is delivered.
Now taking all the money out of his bank while wearing hat, gloves, something over his face. Not sure how it works all over the US but unless you have a very small amount of money in your bank, the ATM's do limit the amount you can withdraw in one day. That means in order to get everything you would have to actually go into the bank and they will not be that happy to help someone dressed up like they are robbing the place. It might even get the banks security involved.
Now as far as running to a village with no electricity, really depends on where you are in the world right? In some countries finding such a village will be easy, in others not so much.
As far as the Princes Security, well just the fact taht you might indeed have Kate int eh room with you and managed to murder her with them intervening might mean they are hopelessly inept. But there is a very good chance that they will in fact be just down the hall from William, pretending not to be there, but ready to pounce on you. But the whole situation does leave this an open issue.
Changing flights, again depends on which country you are in, since some require more passes through security then others and showing up at the airport in a hat, gloves and mask could earn you alot of attention.
The issue of iding you, will of course possibly be made easier by the hotel again depending on which country you are in. I am going to assume that you are not in some seedy dump since you got Kate there and the Prince is not far behind. To get a room you need some ID. So they may know who you are from the start. Depends of course on who got the room you or Kate.
Interesting plan a few holes, but interesting.