You see the content you choose to click on. Should my premium membership mean that Youtube blocks me from viewing Superbowl commercials the day after? Or movie trailers? Premium is simply paying Youtube so that Youtube will not show you Youtube's ads.
You can if you have Premium. If you start manually skipping forward, the UI gives you a ‘Jump ahead’ button that skips straight to the end of the segment (based on crowd-sourced data, it seems).