If you have no cards in hand as Moonveil Regent's first ability resolves, you may still choose to discard your hand. You'll just draw a card for each of that spell's colors. Great plan!

If you cast a colorless spell, you may choose to discard your hand and draw no cards. Less great plan?

The colors of a transforming double-faced card that was cast with the disturb keyword ability are determined by its color indicator, not the mana cost on the front face of the card.

Moonveil Regent's last ability triggers even if you control no permanents that are one or more colors when it dies. The amount of damage is calculated as the ability resolves. Consider only the permanents you control at that time to determine how much damage Moonveil Regent deals.