Not always. There should be state laws that do not allow a driver to come to a stop in the roadway when there is no reason to do so. Here it seems like the driver overreacted to the pedestrians who did not enter the roadway. If your state is a comparative fault state you may argue that the sudden stop was not reasonable and that the driver of the front car has some responsibility for the crash. This will however be an extreme uphill battle and may not justify the time and expense involved. If injuries are minor it may not be worth the effort. If injuries are substantial may be worth a shot.
Not necessarily. Generally speaking, all drivers owe a duty to act with reasonable care when driving. While the following driver was probably following too close, that does not mean that he/she is 100% at fault automatically, and I have seen cases where the driver in front has been found at fault (sometimes even more at fault). Talk to your insurance company, though, to make sure they are on board and can provide you with legal counsel if necessary.
In Oregon, and likely most other states, every driver has a duty to use reasonable care under the circumstances. This means that you had a duty to follow at a reasonable distance and speed. This also means that the other driver had a duty not to randomly slam on his/her brakes in traffic. The claim could turn on the details of how far the pedestrians were from the crosswalk, how far back you were, what your speeds were. You're not automatically 100% at fault but, as noted above, the rear-ending driver has an uphill battle.
Sign up to receive a 3-part series of useful information and advice about personal injury law.