Let me see if I understand:
1- When the bolt is cocked, the safety does not go on. This is an issue.
a- Is the bolt closing all the way? If not, the safety will not work. BTW, on Mausers, when the safety is to the left, the gun is ready to fire; up is safe/bolt can be operated; safety to the right, safety on, bolt locked.
b- Do the numbers on the safety lever match the rest of the gun? If not, the safety lever may have been replaced, and may need to be fitted.
2- When the bolt is released, the "plunger" drops. Hmmmm, let's see. Does this mean that when the bolt is closed, the striker falls off the sear? Or does it mean that when the action is opened the striker drops? The first one is an issue, the second is entirely normal for a "cock-on-close" action.
Either way, if the safety will not go on, it's time for a trip to the gunsmith, and you could have him check out the other issue as well.