From the initial looks of it, I would have to say that your friend has not put very much effort into looking at the class changes for balance druids that occurred in 5.4
- some simple things he can do is regem, reforge, to get some more stats and whatnot out of his gear but honestly that isn't even the problem.
looking at the logs you posted their moonfire and sunfire uptime is 37% and 30%. I think the biggest immediate fix you could tell them to do would be just dot everything that moves if you can target it, apply moonfire and sunfire.
2 fairly terrible trinkets dont help, but his numbers are really...really..low.
He seems to die a lot.
Honestly, I cannot figure it out. DOT uptimes look fine on a per-fight basis. Gear is better than mine in many cases, but he's pulling half the damage...I honestly think he just needs to hardcast more...and press Starsurge more often.
I know I don't post much here, but hopefully I can add some input that could help.
Yes one of his trinkets is not close to being ideal (Yu'lon's Bite) but he can at least make the best of his situation. And from looking over the logs, it really doesn't look like he is maximizing his potential. I'll go through a couple of fights, but I don't really want to spam this post so if you have more questions I will keep going.
1.) His dot times seem to be an issue on a few fights (Protectors). He died on some of the others unfortunately.
2.) He needs to not be using NV in my opinion. It is by no means a bad talent, however there are certain fights (Protectors, Sha, Galakras, Juggernaut, Dark Shaman) where other talents would make a huge difference. I raid 10man, and we have questionable healers sometimes, and I have not taken NV on any fight yet this tier.
We will just stick to Protectors for now, he seems to have died on Galakras, Juggernaut, and Dark Shaman or I could go more into that as well.
To be completely honest there shouldn't be any reason for him to have an 83.5% uptime on Sunfire, especially on a multitarget fight. He doesn't seem to be making use of his SS procs, now I'm not sure of your strat and if you stop and certain times or w/e but either way; having a 49.4% 'soaking of SS procs' is not good. Especially with how they reduced our chance to get procs from dotting multiple targets. One major point, the correct way for our dps to look (sometimes could be skewed depending on what you're doing on the fight) is Starsurge to be your #1 source of damage, followed by your dots. It looks like he is just not using the ability when it comes up.
Have him do lfr and practice DoC/Inc and Fon/HotW, they are very useful for a lot of fights in this tier.