Google's algorithm (which Strum seems to be pollinating everywhere -- and good, because the old algorithms were failing DARPA tests) is to pre-map the road. The car knows exactly where it is and what is supposed to be there, which it also compared with what it sees now.

How will it react to a bicyclist running a red stoplight and into the car's path, when the car has a green light?

It will stop. In fact, the "failure mode" of self-driving cars will be how pedestrians can bully them by stepping in front of them so they stop.

When the car comes across kids playing football/street hockey/baseball in the street, will it stop for them?

There is already video of this. The radar/lidar isn't good enough to see a baseball, but it's definitely good enough to see a kid.

Will these cars have systems to react when they take damage?

It will probably pull over and stop if something is wrong.