I don't know the exact distance, but the safety is supposed to move the cocking piece back off the sear. Yes, there is a safety spring and plunger (not a ball) that holds the safety in position. You don't say if you have the pre-64 or post-64 but they are basically the same, though the layout is a bit different.
The parts can wear with the result you describe. If you are not familiar with the way that safety works and takes down, I suggest taking the rifle to a gunsmith. Most parts, even for the old model are still available.