The question of FMGS vs FAC derived speeds has raised its head again in this thread. The FAC weights can be in error by a very large amount depending on the signal from the AOA probes from which they are estimated. 0.1 degree error in the AOA probe can give errors of up to a couple of tons!
There is absolutely no need to use anything other than the FMGS weights and speeds unless a "Check gross weight" message is received. If in doubt, you have the loadsheet to rely on for your ZFW plus the fuel remaining to calculate the current weight. Anyone attempting to use the FAC weights in flight is asking for trouble and it is specifically not recommended by AI.
The trim wheel is indeed almost useless in flight, except in Alternate Law. It is not even very accurate for takeoff but the autotrim system will look after you once airborne, provided all is in working order.