There's not a whole lot I can say about the AoE thing that hasn't already been said but there are a couple of things I can add. I know that it can be difficult to watch for the cast bar during boss mechanics when there is a lot going on, especially for a healer because you're tasked with both watching the boss and keeping people alive. My advice is to be patient. Once you really begin to articulate mastery of your class, it should help with your overall awareness of what's going on and help deal with encounters better in general. It is worth mentioning, however, that latency IS a thing in this game and can't be ruled out completely. I'm pretty sure this has long been fixed, but back when Titan HM was current content, a lot of people were struggling with it. There was an issue with weight of the land where you could get hit by it even if you were clearly not standing in the telegraph. I'm not saying that latency is 100% of the problem but it could certainly be part of it.

For the gathering, I can provide some insight. I read somewhere quiet awhile ago (I don't remember where) that the sometimes wonky crafting and gathering RNG is the result of the system Square uses to determine the rate of successes and fails. Evidently, their system is inferior to the way other games handle RNG mechanics (you would have to ask someone in general discussion for a more thorough explanation). I know this because I looked into it myself a few years ago. What you are describing used to piss me off as well.

I hope I have been of some help. It would be a shame for you to quit the game when it's such a great time to be a part of it.