1. How do we know they’re not going to kill us?
This is going to be macabre, but it needs to be stated: self-driving cars will definitely kill people. That’s a statistical certainty. That said, they’ll kill way fewer people than human drivers do currently.
2. Are they safe?
It's hard to define what exactly "safe" is. When you crash into a tree, it’ll be the same as any new car because it’s still subject to the laws of physics. That said, you probably won’t crash into a tree, so yes, they’ll be safer than you driving your own car. No, they probably won't be as safe as airliners, mainly because planes are inspected for faults every single day.