For starters the safety is not functioning properly. It engages in the safe and not safe positions, but not automatically when the gun is broken open and closed. You didn't say, but does you gun have a single trigger, If so, there is no safety push rod as there isn't room; and all FW frame Smith single triggers operate manually.
Also when the gun is broken open, the toplever/rotary bolt will close while the barrels are fully open. Sounds as if the hold-open spring was not replaced, or is hung somehow in the compressed position.