Re: similar looking aircraft
Aerodynamically speaking, I'd say that there are currently four basic forms: fuselage-based, lifting body augmented, flying wing (FW) and blended wing-body (arguably, BWB is a subclass of flying wing).
As far as fighters are concerned, fuselage-based is the oldest form and is used in all of the current U.S. fighters (F-15, F-16, F/A-18, F-22 & F-35). Lifting body augmented was first used, in a fighter application, in the U.S. F-14, and was also employed in the YF-23, but now is only used in the Russian MiG-29, SU-27 family & Sukhoi T-50.
In the context of fighters, both flying wing and Blended wing-body suffer from poor yaw control, but are being tried in some 'agile' drones.
The important thing though, is that any spying will be directed at the electronics fit, not the aerodynamics, and so will not be reflected in the appearance or form of the aircraft.
The appeal of stealing details of the F-35 is that it will make it possible to screw not only its flight & fighting systems but also its logistics & maintenance systems.