(a) That's incorrect. For a transfer of Torrens system land to be effective in giving the buyer legal title to the land, the transfer must be registered. In a transfer of land, payment of the purchase price is irrelevant to the question of when legal ownership passes to the buyer. But as a matter of practice, payment usually takes place at the same time as registration so that both parties' interests are secured.
Registration of title in the Torrens system has important legal consequences. It gives the registered titleholder 'indefeasible title'. The word 'indefeasible' means that something cannot be defeated, challenged or made void. Indefeasibility of title therefore means that, except in limited situations such as fraud, the person registered as owner of land has a paramount, or indefeasible, interest in the land.
Registration has the effect of curing (rectifying) any defects in the previously registered owner's title. This means that the buyer obtains clear title to the land. A person who may have any unregistered interests cannot enforce them against the new registered owner.
If rights in land are not registered, the holder of such rights only acquires an equitable interest. This means that their rights are only recognised in equity, and only equitable remedies are available, which depend on considerations of fairness in the circumstances. An equitable interest in land is less secure than a legal interest.