That is an extremely complicated question.
I think first you need to understand WoE basics; the purpose behind WoE and the aim of it.
WoE is guild vs guild, (compared to pvp being party v party), and friendly fire doesn't happen to guildmates/alliances (there are exceptions but that's not for now)
Damage is reduced greatly. Ranged and skilled damage is reduced by 40% iirc. And with the right gears you can reduce damage even further.
So on top of that a lot of player skills are mitigating the damage. See the Magnetic Earth? (the big white blocky skill under the players) that is blocking all the magic damage. Paladins have a large hp pool and will sacrifice their party mates to take the damage... a lot of WOE is just potion spamming also.
So really about not dying, it all depends on
- how your party is set up and what skills are mitigating the damage
- your equipment
- how many potions you can spam
Asura hurts, but it's ok because some (very expensive) gears can reduce it to nothing / some paladins have enough HP to live the damage, and also, being one champ running into a mob of people will likely get the champ killed.
Important targets varies depending on the situation and the opposition. Sometimes you just KNOW who the strong/dangerous players are on the other side and take them out first. Other times, you'll take out the people providing important buffs (strings/ME), or just the people you can get who dare get in range. Theres also recallers.
As for making sense of everything, perosnally I hotkey /effect to toggle effects on and off so I can see. A lot of people run a program called RCX (on classic only) that allows you to see the spells on the floor without effects on. It's allowed, but it's not an official program.
Everything else just falls down to experience. Ask your guild to teach you?