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DnD updates dynamically, best time to use it is on CD, but if a feather procs and the CD is up, you get the most damage by using it at 10 seconds into the feather proc.
Yes, it's worth reapplying, and you get the most gain reapplying with 10% or more AP then your current diseases. Check out DKDoTs or DKDiseases, both great addons just for that purpose.
Let's say diseases naturally last for about 60 seconds, and shadopan has an ICD of 75 seconds. To extend it an extra 18 seconds would "cost" 6 SSs, and you'd gain 3 FeS as well.
79295 x3 FeS =237885
94020 x6 SS = 564120
That's a cost of 326235 in 541 gear. How much damage would you gain? Shadopan gives about 9k str, *1.05*1.05*1.10*1.15*2.2~ 27.5k AP. Diseases scale with 0.158 AP (*2*.5mastery) = 0.449 AP, So diseases would hit for about 12.3k more per tick. 18 seconds is 6 ticks, so you'd gain 74k damage from diseases. We also save one reapplication though, and therefore one SS at the cost of one PS. That's another 55k, putting the total at 129k (extending diseases) vs. 326k (not extending diseases)
So no, not worth it. It is worth reapplying when shadopan comes up.
Too early to tell. Blizzard might nerf feather, but there past treatment with trinkets that are too good to replace (darkmoon card greatness anyone?), and GC's recent tweet leads me to believe that they don't have a huge problem with trinkets lasting more than a tier. That being said, if every other class is upgrading to a more powerful trinket, and we are not, there will be small power creep.
Death knights are in a pretty good spot right now, and losing the advantage of feather will not make us "need" a buff. We won't be constantly topping charts, but nor should we be rock bottom. I don't expect any major buffs or nerfs for dks in 5.4, we have already gotten quite a few QoL changes (that are awesome BTW), and we should be very middle of the pack in 5.4
And there is nothing wrong with that.