If a turbofan engine can create more thrust than a standard turbojet engine, would a turboshaft engine benefit from using a turbofan to power the shaft, in a hybrid kind of set up?
Cutting some corners to keep this simple but:
Turbofans make more thrust than turbojets, because they employ a large fan driven by a jet engine. This way it can accelerate a large amount of air, and while the acceleration is less than what a turbojet engine does to the air that passes through it, the efficiency is greater anyway. Accelerating a large amount of air a little is better than accelerating a litte amount of air alot.
Turboshaft engines are basically jet engines that convert pretty much all of the energy of the exhaust jet into rotational movement, which is then routed through a gearbox to drive a propeller, rotor or whatever needs to be driven.
One could say the core engine is the same in all of the three cases here, what varies is how the energy of exhaust jet is used. Turbojet simply relies on the high speed of the exhaust as it is, turbofan uses most of the exhaust energy to drive the fan, and turboshaft uses all of the energy from the exhaust to drive the output axle (and gearbox).
A turboshaft run by a turbofan makes little sense. It's like running a car with an outboard motor.
What you may be thinking about is a geared turbofan. They do exists, this engine employs a gearbox to reduce the rpm of the fan driven by the jet engine. This enables the use of larger fans, as the fan blade tip speed stays lower even though the blades are longer.
Turboshaft produces torque, not trust. It is a turbine with a power shaft or an accessory drive. It uses the torque to produce thrust, but there is a variety of power consumers, for example, a helicopter rotor or a ship propeller.
turbofan is a turbine and a fan. The turbine produces torque and a bit of thrust, the fan produces thrust.
There is also turboprop which is a turbine with a propeller.
Effectively, they are the same core with different power consumers. Plus, turbofan also utilizes the power of hot exhaust gases.
This answer goes into more details on differences between turboprop and turboshaft and how they are used - and more.
I’m not sure what you’re asking here. Keep in mind that a turboshaft engine creates no thrust, only power. A turbofan engine does not necessarily create more thrust than a turbojet, it’s just more efficient at high subsonic and transonic speeds. Probably a better way to view a turbofan engine (or at least high bypass turbofans) is that it’s a gas turbine-powered ducted fan, operating on the same principles as the ducted fan engines that you find on some radio controlled aircraft.