…Would it affect their turn or not? Would they draw 3 before rolling the dice? So if they then roll the dice and get, say, a Draw 5 would that affect the Draw number i.e. turn would it become a Draw 8 or would it override the Draw 3, and stay a Draw 5 or would the Draw 3 somehow override the dice roll and cap the Draw at 3? Would that be the same for play cards as well?

A: Consultation with Andy yields this: the Draw 3 recipient would play that card before their turn, as required. With Dice Override in effect, that means they would get to draw 3 cards and the Draw 3 would go in the discard. They would then roll the dice as per usual for their turn.

The three cards drawn for the Draw 3 card would not count towards whatever they roll on the dice, so, yes, if they rolled Draw 5, they would draw 5 more cards in addition to the 3 they drew for the Draw 3 card.

The total would be 8, yes, but think of it as two separate incidents. The Dreams and Omens card is a separate incident that happens before their turn starts. Then they do what their turn requires, rolling the dice, and doing what they say.