Happiness is the result of actions. Actions are sometimes the result of moral rules. Happiness is never directly the result of moral rules alone?

I suppose it can be if you like having moral rules. I, personally, don't like the idea of nihilism.

The term "action" seems to only incorporate intentional behaviour. If someone gets struck by lightning, for example, that can have a serious impact on someone's happiness. But was it brought about by an action? Not really. That's why I think we need to widen our scope to include not just actions, but all events. In principle, anything that brings about happiness is good, wherever it comes from.

I suppose act utilitarians have argued along the lines of your first post: rules cannot create happiness except through acts. Let's cut out the middle man and act as best we can. Rules will only get in the way of our choosing the right acts. However, it's not that simple. The right acts must be chosen one way or another. We can't automatically favour deliberation over rule-following. If we were able to apply all the knowledge in the world to a problem instantly, we should deliberate in this way before making any decision. If, on the other, hand, we had no intellectual ability at all, we should follow rules entirely, never thinking for ourselves. However, we fall somewhere in-between, so we should deliberate only in so far as it'll increase happiness.