Can you push the throttle forward while using reverse thrusters (for turbofans)? Does this have any effect, such as strengthen the "reverse" air blanket? Is it ever used?
On typical Boeing throttles, this example being a 737NG but similar on all Boeings, the reverse thrust levers must be lifted to engage reverse. In order to do this, the thrust levers must be in the idle gate and cannot be advanced until the reverse thrust levers as stowed. The reverse levers engage locks in the thrust levers. In this video, at 2:50, you can see the thrust levers being retarded to idle, then the reverse thrust levers being pulled up. At 3:22 they are stowed.
In this video from an A321, you can see that the Airbus system is very similar.
In the B757 aircraft (RR engines), for example, the "reverse" thrust levers can only be raised/employed when the aircraft is on the ground and the "forward" thrust levers are in the idle stop position. During reverse thrust operation, the forward thrust levers cannot be pushed forward.
This is different than many Turboprop airplanes