Just a few comments, take them as they help.
Gearwise I think you're doing alright. FSW set, spellstrike pants, holo-gogs are all good. Going for the badge cloak is a good idea, but I would suggest trying for the Handwraps of Flowing Thought off Attumen or the Studious Wraps badge item. Try for a new trinket to replace the Violet Badge (dam is always helpful) like the Icon of the Silver Cresent or something similar. You may actually have something but your armory is showing the Violet Badge.
I won't give suggestions on gems since I am no expert, but your build I think I might be able to help with. I think the one I see now is probably your PvP build (17/34/10). I'm new to PvP so I can't help there, but raidwise I can help.
Affliction or destruction own in raiding (demonology only if you know how to micromanage your pet). For my raids I use a 42/0/19 malediction spec which works pretty well for me. Check out my profile if you're interested. For raids you should stack hit...you getting 5th on that list may have something to do with resists...55 hit means monstrous resist rates in any raid. If you want to go pewpew destruction....well, I shall leave that to others more informed than I (only specced destruction once...hated it).
Your shadow damage is actually very good, so that isn't the problem...spell rotation really doesn't matter much, but I always go Imm, UA, Corr, Curse of Agony/CoS/CoD, SL, SB spam...rinse and repeat. As aff I macro my trinkets to my dots and SB which gives me a boost of damage. Simple /use 13 /use 14 (I can post them if you want). Also, stopcasting macros and quartz (or some other cast bar) work wonders for lag issues.
Trying to do raid and PvP is quite the balancing act and I'm trying my hand in it as well. I would suggest affliction and run with it for a while then try out destruction and run with it for a while. Personally I love affliction because it gives the raid the boost in dam, cc when necessary, and the mobility that many fights are required to have. Plus, I usually rock first or second on the damage list which is always a bonus.
