Kingdom. forced: After your turn begins, heal 1 damage to your capital. Does this mean that the damage has to happen prior to drawing resources and cards or can it be played at anytime during your turn? Reason for the debate is because of the other cards that say "at the beginning of your turn" take the action.

The answer to Your question is under the "General" paragraph of the FAQ ;)

All instances of “After your turn begins” should read “At the beginning of your turn.”