Aperture has nothing to do with the sensor. It's strictly a lens measurement. Sensor size affects the cost to build a lens with a given aperture (cheaper for smaller sensors, though that tends to balance out due to the difference in enlargement), but the sensor doesn't affect the actual aperture.
Actually yes it does. the Aperture size is relative to the spread of light that falls on the sensor/film/recording space. As the F number is the focal legnth, it matters how big the sensor is to define that focal legnth.
Actually no, it doesn't. You can have a 50/2.8 on a crop frame camera or on a full frame or a medium format. The different sensor size may dictate different lens construction due to the larger image circle, but it does not dictate the focal length, the aperture, or the ratio between the two.
And the F-number is not the focal length. It's the ratio of focal length to absolute effective aperture size.
f2.8 on a cameraphone =/= f2.8 on an SLR =/= f2.8 on a Medium format camera.