The button to lock the door on this old Schlage knob is stuck, and I am assuming I need to take the knob off from the inside to inspect and repair it. However, I cannot figure out how to remove the knob or cover. The screws on the ring have metal caps over them and are not accessible. The divots on the side of the handle that some sources say to press to remove the lock are not holes - just shallow divots. I can't see any other mechanism to remove the lock.

Is there any secret way other than brute force?

My front door has an antique lockset. The round portion where the key is inserted has begun to spin when attempting to turn the key. The bolt also does not full-retract when the key is turned and the key often gets stuck and is difficult to remove from the lock. What do I need to do here? Is there something I can do to get it to be functional again? Failing that, can part of the locket be replaced in order to.leave as much of the antique one as possible? Many thanks In advance.