so from the ground, how many different heights can you jump?
Based on the tests I just did: you need 53 upwards range minimum for a stick jump, and jump height maxes out at 79 range up (higher values do not yield a higher jump past this point). So if each range yields a different height, that's 15 different jump heights. Then there's a shorthop with a C button (which is shorter than a 53 range stick jump), and a C button shorthop while moving sideways, which totals 17 different jumps heights.
I might have messed up somewhere though.
I am assuming that a full hop with a C button (sideways or not) = some stick jump between 53 and 79.
Note: You can actually jump with a Y input less than 53 if you are going sideways and your X input is high enough (weird, X input affects minimum range needed), but a jump done like this doesn't seem to go any higher than 53 range so I disregarded it.
Are full hop c-stick, full hop analog, short hop c-stick, and short hop analog all different?
Yes. Although, keep in mind that there's no solid barrier between full hop and short hop with the analog stick, because it just goes from 53 to 79, that's all. There only is with the C button, because letting go of the C button within 4 frames (IIRC) is what results in the lower height in that case, so when it comes to the C button it's a concerete yes/no for the question "did I short hop?"
Do running jumps shorten all of these?
Yes... except full hop analog is only sort of. Going sideways naturally reduces your Y input (straight up is higher than diagonally up), BUT if your stick's Y input reaches 79 anyways you will get a full hop regardless (not sure if a N64 controller's range is high enough for this to be possible on console).
Also, if the range of the stick is increased/decreased does it change the full hop height?
Yes, but as I said, only between 53 and 79 range.