Petrified wood cuts and polishes like most other quartz minerals. The claw looks like heat crackle quartz.
With all the "cracks" it doesn't look like jade.
The stone has been removed,probably when the piece was repaired and it may not be the original stone.
The "marks" look like solder.The piece originally was shorter,but someone untwisted it.
Mark upside down? Lower right looks like a D.
Size,printed names on object,photo of both ends????
The fossil is an ammonite of some type.
Separate names with a comma.