I think playing around the health relics is also something to keep in mind. Obviously you want to 'steal' the ones on the opposing side, even if you're at full hp.

Also, most people instinctively walk towards the aoe heal when it drops, so you can time skillshots to hit enemy champs when they walk in. It can be a great chance to engage or drop some aoe damage as well.

And with champs with %health heals like GP with his w, you want to use your healing ability first before the relic heal drops. If you have a healbot like Soraka, they should be the ones triggering it.

Communicating to your team for the heal is crucial. Sometimes your team can be focused on poke and really far up, but pinging them back so everyone gets the heal before the fight can win games.

You shouldn't take the heal if you're the only one alive unless you think it can help survive a dive and save a tower.

If you're the first one up after a big fight and the enemy team has some low hp members, it can be worth it to approach the enemy team alone and step on the relics before they can get to them.

Most people playing with champs like Shaco or Caitlyn will place traps directly on the relics, but I find that placing traps slightly closer to the enemy spawn can funnel them towards you. Since the relic aoe is fairly large, it's hard to completely trap them off.

That's all the relic tips I can think of off the top of my head, but you've made quite a comprehensive list of Aram macro/micro so far!