NorBn is spot on with his identification of the beret badge. At one point the Germans used to have bullion for officers versions and metal for enlisted ranks. This applied to other items on the dress uniform, such as the unit patch and awards. But now it's fancy bullion for everybody
The one on the left is DDR "Pioniere und Flugplatzwartungsdienst, LSK/LV", which is basically an airport construction and maintenance speciality badge. It goes on the lower left sleeve cuff of the service uniform. The person selling the thing as Grenztruppen is incorrect.
The one on the right is BDR (West German) "Flugsicherungs und Einsatzpersonal", which is (I think) airbase security forces. It also goes on the lower left cuff of the service uniform.
I like finding uses for expensive hardcover books