According to the rules laid in Vinaya Pitaka, should a bhikkhu arrive at a family residence and be presented with cakes or a cooked grain meal, how much can they accept?

Two or three bowlfuls if desired, taking more should be confessed.

The correct answer is Option 2 - Two or three bowlfuls if desired, taking more should be confessed.

The following  regulations are outlined in the Vinaya Pitaka, governing the conduct of bhikkhus within the Buddhist monastic community:

If a bhikkhu creates a new felt (blanket/rug), it must be retained for at least six years. If they acquire another new felt before six years, regardless of the disposition of the first one, and without authorization from the bhikkhus, it must be forfeited and confessed.
If a bhikkhu is offered cakes or cooked grain-meal at a household, they may accept two or three bowlfuls if desired. Taking more than that quantity must be confessed. After accepting, the bhikkhu should share the food with other bhikkhus.
When a bhikkhu arranges bedding in a lodging owned by the sangha or has it arranged, they must put it away upon departure or have it put away. If they leave without putting it away or without proper leave, it must be confessed.