FLHook essentially is a set of DLL based plugins that allow for added features and commands ingame.
Basically nearly all the commands on the server are based on FLHook.
Soon there will be player built stations, jump drives, cloaking devices and more, all thanks to FLHook.
It also produces a possibility of linking 2 servers together, allowing for the roughly 200 player limit to be bypassed as your ship and you are instantly transported to the other server.
The shortest route calculations are all done by the game using files, not online in particular.
However with FLHook, it's possible to change prices of commodities, availability of commodities and various other things. This means some things are changed on the server that FLCompanion cannot account for.
At least until they fix the option to pull prices etc from the online game.