aa/ an amp only (on the audio out) produce a better improved sound and not just amplify it?
---yes. the amp will give more voltage to your headphones, letting you hear frequencies previously not heared due to the lack of power comming from the soundcard. sound will be more detailed, volume will be enough, the headphone's true capabilities will be shown.
bb/ a dac/amp (on the audio out) trigger the dac and amp or just the amp hence the sound would be the same as aa/
---just the amp since you are on audio out. if you want to use the dac, connect it through usb, and set your audio settings to use it as the sound output.
cc/ a usb dac/amp produce a much better sound than the above aa/ setup
---yes. prob 99% of external dacs are built with better components and capabilities than any default/built-in soundcard.