How tight should brakes and shifters be on the handlebars? How tight should handlebar components be? 

Here it's said 6-8Nm. However, I don't own a torque wrench at that range.

Should the brake levers and commands be tight, or should they be able to twist, so that in the event of a crash, they do not break?
It depends.

On a road bike you'll want them fairly tight to be able to ride on the hoods without the brake levers turning away or moving downward on the bar.

On a mountain bike, at least the brake levers should be able to rotate away in case of a crash. But they still should be relatively tight such that they don't turn away while braking or because of bumps. Depending on where you ride, I'd rather have them a little too tight than lose the ability to brake because the levers are somewhere they're not supposed to be. As a rule of thumb, you shouldn't be able to rotate them without applying some force, similar to opening a pickle jar.