Can these options be changed so that it says “vpre=slow” and “preset=slow”? (Or “vpre=veryslow” and “preset=veryslow”). Are “slow” and “veryslow” valid options?
What do these settings mean, do they matter, and will changing the settings (such as changing “preset=medium” to “preset=slow”) affect the quality of the video?
Is there a list of all possible preset options for the “other” tab, and what they are? (Options such as “preset=fast”, “preset=medium”, etc.)
The meaning of preset as a speed is common sense if you ignore the details. If you want to know the details, see the x264 project assuming you are not using hardware encoder.
That is basically impossible as I doubt anyone in the world knows them all without doing a study and documenting them in one consolidated fashion, and then the information changes as the software and hardware changes. The options are based on FFmpeg, the formats and codecs chosen, and third party codec library that has been integrated.