Murph is distraught when she finds out that her father will be going into a black hole. Her father explains to her that time is slower in a black hole, so things will be different than what she thought.
Space weather is how the environment around the Earth and solar system may vary because of activity at the sun. The Northern Lights is a harmless example of space weather. It is an effect of an event called a Coronal Mass Ejection or CME.