Fix broken screw hole on outlet box
You can try putting a toothpick in the hole and see if the screw grabs better. You can also try a bigger screw.
To replace the box, remove the outlet and untwist the ground wires. Straighten out the wires and bent out the tabs holding the cables in the box being careful not to damage the insulation. Turn the two screws on the box counterclockwise while pushing the screws inward. This will turn the tabs that secure the box to the wall allowing you to pull the box out. Work the cables out of the box. Get your new box, insert the cables in the box, place it in the wall and turn the screws clockwise to raise the tabs securing the box to the wall. Twist the grounds together and connect the outlet using the terminal screws, not the backstabs, and attach your ground wire.