I think you need to look at some objects... and you'll see there really aren't any classes to use...
as for functions, again not many that you will use, if you look at existing objects you will find the ones you are after
but if you want a list...
look in the firmware directory, look at the axoloti_*.h header files.
of course using can also potentially use chibios functions.
the parameters are defined in parameters*.h and ui.h
for some of these things though, you will need to start looking at the code, to understand how these things works.
as for types, between objects, they are all int32_t, its just how they are interpreted.
(Q27 or Q31, you may want to read Q Number format
as a programmer, I know what you looking for, but once you dig into to axoloti, you'll see what your after doesn't really exist. its closer to the metal, not really an abstract api.
(thats not to say there isn't room for improvement on documentation if someone is willing to take up that challenge!)