I would start by making the mouse visible during the menu parts. When you go through a door, it also randomly moves you to either one of the other doors, making it very risky to use them. Just make sure the doors don't randomly pick one of the other doors to move you to, but instead always move you to the same door.
Zombies can also spawn very close to your position, killing the player instantly. I am not sure if the zombies could use the doors, but the bullets didn't interact with the doors. If you replace the doors with portals you can let bullets travel through them.