I'm about to start Operation Cyclone, and I'm unsure about the placement of the cover elements. Unlike in Blue Thunder, none of the Cyclone scenarios specify which player places the cover elements. Is it always the Defender, or do I just follow the standard rules and each player places half of them?

And is there anything stopping the defender from placing the tank traps at the entrance to the landing crafts, thus blocking any tanks without Jump from coming out?

Yup, unless stated otherwise for a specific scenario, place as per rulebook. And its fine to place traps wherever you like in the determined set up area for them.