The biggest favor you can do yourself is to tackle fights with an idea of just healing. But pay attention to the instances where you don't need to heal. These are the places where you can safely insert dps. You can start with something as simple as the Aero DoT and insert some Stones if it's single target and some Holy if it's multiples.

WHM has strong heal over time in Regen and Medica II, so this can tick away doing a lot of the healing for us and allowing us to slip in that dps. If you take this approach, you won't fall into the tunnel vision mindset some healers do and find yourself not able to react well if unexpected things occur. We don't mitigate damage. We react to it. And getting comfortable with the amount your heals do, how effective your HoTs are, and studying the flow of the fight will allow you to easily drop out of dps mode to drop a heal and slide right back in again with little trouble.

So use your HoTs, keep your party's health at a decent level, and slip in dps when you've got windows where nothing is happening and you'll get comfortable with flip flopping in no time.

As for Cure II, I is still a bit useful after you get Cure II if you're in a high healing situation. If you're able to use Cure II as the primary heal and not be out of MP, go ahead and switch. Otherwise use Cure I as you need to. You won't really need it at higher levels since if there isn't immediate incoming damage, you can drop a Regen to do your work for you.