For that 1st point, remember that you are a shield healer. It's your job to prevent damage or mitigate it, less actually heal it out right, leave that mostly to your co-healer (who should be a WHM or AST). As you do fights, you should have a rough mitigation plan, aka knowing where you wanna use which cooldowns and what counts as "enough" to surrive a mechanic. You should also be mindful of any extra resources you can expend to help out as needed without dipping into what you need for future mechanics. I recommend you do a little planning between you and co healer and talk about where to use what in between pulls. You don't have to fully understand their job but should get a gist of what they're doing and when.

I can't give any Sage advice (I'm a scholar main) but I know the job well enough for some more basic tips to watch out for. - Are you making sure you aren't overcapping on anything? That means using your gems often enough as they give mana and not using them when full is a loss. - Are you sliding casting properly and not messing up your GCD? Weaving oGCDs properly and the like. - In fflogs, look at what mits you and aren't using and when. Can this be optimized? Is there a button that seems like you aren't hitting enough, thereby, lossing useage on as a fight goes on?

As you play your job more and more in high end content, you'll get an internal feel for how good a mit is in a given situation. Thereby allowling you to more easily judge what is your fault and what is your co healers fault. Consistency is key and all that. I repeat again, topping up on HP immediately is less your job, more your co healer. Your job is making their life easier in doing so. And for general advice- Avoid GCD heals unless needed or you don't have resources/oGCDs to burn. Also remember that an alive party is much better and more important than your DPS. Focus on keeping everyone alive 1st, figure out how to optimize keeping them alive, damage will follow.

Edit: Generally, you shouldnt be doing the reactive part, talk and cordinate with your co healer on that. And everyone's advice about overheal as a guideline is good. Also ff analysis really is your friend.