[Accurate Ametrine] is probably your best bet in yellow slots, giving you both hit and exp to raise your crit cap. Probably best til exp cap is reached.

AP vs. Haste

I know that AP > Haste in lab conditions and encounters with no interruptions for mutilate. But what about other encoutners? Should I still favor AP over Haste? I now use Herkuml War Token, which imho favours haste a bit as well.

Everyone is slightly different. Through my spreadsheets, I know that ATM, MY personal EP weight favor Haste. I would check your spreadsheet to verify.

Using Aldriana's spreadsheet, I believe that it automatically calculates your EP weights as you change your gear.

I've checked the spreadsheet, and it now favours stark ametrine in yellow slots when there is a bonus. But the question is still, would it be beneficial to use more haste in case of moving/interrupting/adds bosses over AP? (like in a blue slot, no bonus).

Fight lasting 4 minutes. What will be more favourable: use vanish 2 times for fight (but it will not get under various procs) or 1 time but under trinket, berserk etc. Trinket - skull 264.

The basic rule for using vanish with buffs/procs is: time them together if you're not losing a vanish. The extra DPS of a second vanish will vastly outdo what little extra DPS you squeezed out of timing vanish with all the right procs. Besides, if you use vanish right at the beginning of the fight, i.e. as soon as Overkill's 20 initial seconds are over, the odds are quite high that you'll have quite a few interesting procs up, as at the beginning of a fight nothing is on inner CD yet.

I'm not fully sure if you're trying to ask which is better, or which is better for movement heavy fights. Your sheet will tell you which is better in the perfect tank and spank vacuum. As your haste goes up, the relative weight of haste will go down, and similarly with AP. The other stats will affect them in less obvious ways, but it basically depends on how much "passive" haste you end up with on your gear. If you get a ton of nice gear with haste on most slots, you'll probably find that AP is worth more, and vice versa if you don't have much "passive" haste. So just check the sheet to see. If haste is over 2.0 then you're better gemming that in most cases, and if it's under, you're better gemming AP where possible. If you're in a similar gearing situation as me, you may find that haste ping-pongs around 2.0 with every slight gear upgrade and different gem type you use. In this situation you just want to gem whichever is higher until haste tips to the other side of 2.0, and then gem the other stat. Obviously you won't regem 15 gems every time you get a new piece, but if you find haste is 2.2 with a new piece of gear, then you should gem it with as much haste as you can fit in, similarly, if haste drops to 1.8 with your new piece, you'd gem AP.

As to the other question you (might) have asked, I'm not sure which stat is best compared to the other on movement heavy fights, but I'd put my money on AP, if you're just asking about which is better in theory. Movement heavy fights will weight your overall damage towards yellow damage because you lose a ton of white swings while moving but your energy still pools. So unless you have an excessive amount of time off target (which doesn't really happen) you'll still get to use basically "all" of your energy on yellow attacks, while missing a good chunk of white damage. So once the damage leans towards yellow over white, I would guess that AP pulls ahead in theory. AP contributes directly to all yellow damage where as haste only sort of indirectly contributes (via your energy regen talent).

Still not sure exactly which question you're meaning to ask, but hopefully that answers them both.

I'd suggest to judge the individual situation. Depending on the fight at what's going on around you, a Haste pot might be better spent when a burst is needed, than when you get the most overall DPS out of it.

For a 'Patchwerk fight', using a Potion of Speed in conjunction with as many Proc's and cooldowns as possible is the most beneficial for you. What matters is how many buff effects you can stack ontop of one another, especially Berserking, Blade Flurry (multiple targets), DBW and Heroism.

What matters isn't really Heroism/Bloodlust or Blade Flurry alone (assuming single target ofcourse), since all haste effects are additive. What really matters is Berserking, DBW or other proc's that give you stats other than haste. Haste doesn't make your existing Haste "better" than it already is. More AP however, makes your Haste better and vice versa.

Which is wrong, as all haste effects are multiplicative except haste rating, which is additive.
Thus Heroism, Blade Flurry and haste rating are multiplicative, whereas the haste potion only adds additively to your haste rating.

However, this is no answer to the original question. I'm myself unsure what the very best practice is, so I react to the circumstances. If my procs are running right now, and will end before Heroism will become active and have no chance to overlap during its uptime, I use the haste pot then. However if there's a good chance that a (strong) proc is active during Heroism, I wait for it.

Not necessarily the best, but it may be a decent guideline.

So you could technically say there are 2 different kinds of haste and that they both don't effect one another. i.e. hero/lust, Blade flurry, SnD are different kinds of haste additives than haste rating , i.e. Potion of speed, or haste proc from a DBW

As does, for instance, Mongoose. All haste effects that simply give a percentage multiply with each other; all haste rating adds together and then multiplies in as well.