High bypass turbo fans like airliners do get a significant bit of the compression from the forward momentum. They will never be able to function like ram jets, but the momentum makes a big difference especially at high altitude where the air is less dense and there isn't as much to suck in from the fans/compressors alone. The high bypass engines of the airliners will function much more efficiently at high altitude because of this than that of a low bypass military fighter, however it won't be able to achieve as high of a top speed as that same fighter under the same conditions. Basically the low bypass gets the advantage of speed while the high bypass gets the advantage of fuel efficiency, but both greatly benefit from momentum based compression.

Yeah, most of the squeeze is done by the forward momentum of the engine through the air. And at a certain speed (~mach 3) you don't even need compressors, it will act as a ram jet, which is what the SR-71 would do as well as the fictional DarkStar in TopGun Maverick. It's certainly MUCH more complicated than how I explained, I just did the basic principles of it.

Yup, but the concept is still very simple at its core. Follows the same 4 stages of a traditional internal combustion engine like what's in most cars. Suck, squeeze, bang, blow.

The fan and the outer stages of the compressor is driven by the turbine and sucks the air in

The inner stages of the compressor squeezes the air.

Fuel is mixed in and goes bang in the combustion chamber

The burnt exhaust gas blows out the back and spins the turbine

Turbine spins the fan and compressor and the cycle continues.

The fan essentially functions like a propeller that's enclosed by an engine nacelle. Just instead of the fan being turned by engine cylinders like on a traditional propeller driven piston airplane, the fan is turned by the turbines in the jet engine.