Anti-Rattle Clip - and you can drive without, but not a good idea, as the pad will move around and could case damage to the pad if left over time. Get the dealership to replace it for free. Tell them it fell off.
Sounds like it wasn't installed properly.
The mushy break pedal is a result of the mechanic not re presurizing the system properly. They are suppose to do so and test drive the car to make sure it works ok. If they are fine now, they are ok. No need to worry about it.