Is the commission still due if the contract is annulled or conditional?

In general yes; with a suspensive condition, only when the condition occurs. With a resolutive condition, the occurrence of the condition ends the contract’s effects, but the fee is still due. The fee also stays due if the contract is annulled or rescinded, unless the agent knew the ground for invalidity (Civil Code art. 1757). Check how conditions are written in your contract. Full guide: who pays the real estate agent’s commission in Italy.