A330 GWCG on ECAM
 

How does it calculate it's GWCG on the ground before take off? I know it get's its GW from the ZFW and BLOCK fuel which is entered into the FMGEC.

Is it worked out by the THS setting from the load sheet?

Am I correct in assuming that it recalculates it dynamically in the air by using the alpha vanes?

FCMC GW and GWCG rely upon ZFW and ZFWCG entries in INIT B. Fuel quantity is measured by FCMC.
For the calculation itself, I assume it (FCMCs) compute it as you would do on a manual LTS. No THS involved for that computation.

FE GW and GWCG calculations are a bit more detailed in FCOM 1.22.40p4:

FE Weight computation (back up)
When the aircraft is below 14625 feet and 255 knots :
GW = f(alpha, CAS, N1/EPR actual, CG from FE part, altitude)
When the aircraft is above 14625 feet or 255 knots :
GW = TOGW - WFU
TOGW: takeoff gross weight
WFU: weight fuel used acquired from FADECs.

FE Center of gravity computation (back up/aft cg computation)
The CG is computed from the position of the horizontal stabilizer and is function of the N1/EPR, Vc, ALT, MACH and GW from FE part.