Plenty of tips will come so I'll just give my two cents on what I had to learn through my mistakes. I guess first is learn to trust your fairy and when to use which. A lot of people will say use Selene all the time. But nowadays I fins myself using Eos more than ever. Her rouse + regen lets me stay in cleric even when the tank starts taking a but more damage. DPSing is key to being a SCH and finding that sweetspot when you know to go back to healing will help a lot. The kit revolves around this. SCH have no real big heals and the closest one is gated behind aetherflow. So mitigation and proper fair use is key to keeping people alive. Gotta be proactive.

You'll be wanting accuracy since a large part of being a SCH is DPSing and missing broils can make you cry haha. Crit is nice too, if you can afford to put it in but many of the 220/230 gear is already capped with crit.

I have the lore weapon because I never bothered to work on my relic and I still can't lol. Serves me just fine, before this I had the ESO book that I used to clear Seph Ex with but I used the tokens on my other jobs.

In cases that you need to fix a co healers mistakes, its very possible to do. But the SCH is meant to prevent those mistakes through mitigation and your flexibility and near endless mana. As for solo-healing, I'd say it would extremely difficult to solo heal a whole fight, in harder content. But there were plenty of times I had to solo heal for a bit during Seph Ex and it works but I make it my priority to get the WHM/AST up as I know I don't have the power to keep it up for long. SCH most powerful heals require aetherflow and you only get 3 a minute so that's what makes it hard to solo heal. Emergency tactic can turn your shields into sweet direct heals but it has a cooldown of 30 secs. I actually use it quite often, so that I can use my aetherflow on Energy drains or bane or sacred soil.