As for the indicators in battle, try and keep a look out for the casting bar instead. When the bar finishes, if you're in the indicated area, you're toast. So get out before the boss/mob's cast bar finishes.
Doing that you can, more often than not, actually go back into the animation area and keep DPSing/Tanking/Healing without getting hit. Can take a little while to get used to and nail perfectly though.

As for gathering percentages.. that's XCo-, sorry, FFXIV for you. Sometimes you'll miss all 90+% in a row, and sometimes you'll gather all mats at 60+% while getting a HQ or two. Sometimes you'll even make three HQ items in a row at a 1% chance when crafting.
RNGesus is a cruel master.