To me, it looks like you're saying if a unit is cargo and it is either on a city plot (including forts) or it is a transport then it cannot be loaded.
Exactly, I just said so.
If I had a unit as cargo in a ship sitting in a city, it should be loadable onto another transport on the same plot.
Yes, you can do it after unload the unit you want reloading to another vassal.
I intend to make exclusive between "Load button" and "Unload button", because I always confound them.
A pair of "Load" and "Unload" commands confuse me that whether the unit is already loaded onto vassal or not yet.