Everything in regards to WAR optimization depends on the fight. And, because the details of those fights are constantly changing, you will not get a definite answer to your questions.

But, there are some general ideas that govern how you approach optimization.

In regards to your first question, CD management, Berserk and the relevant syncing with Berserk is a huge part of WAR DPS. As such, it's important you get the most up-time out of Berserk as possible -- that means getting the maximum number of activations in a given fight and not wasting any GCDs while Berserked. This varies depending on the length of the fight and the specifics of the phases / mechanics. Take A5S for example. During earlier progression with slower clears, holding Berserk for the small phases was bad because it typically resulted in one less Berserk at the tail-end of the fight. Yes, the boss takes more damage while small. But, a gimped Berserk during big-phase is still better than losing a Berserk. With current levels of DPS and sub-5-minute clear times, holding Berserk for the first small phase works better because of the length of the fight. So, given that you will only get 3 Berserks in a ~5:00 fight, you have a bit of flexibility with their timing. As such, your opener as well as general Berserk timing changes.

Another example of this is A7S. If you are tasked with handling melee jails and need Berserk to do so, you will not be able to fit in a triple FC Berserk opener because the first potential melee jail will happen before Berserk's recast has finished. But, holding Berserk for at least ~80 seconds is horribly inefficient. As such, you can pop Berserk ~8-9 seconds before the pull, settle with a double FC opener, and have Berserk ready for the first jail set. After P1 jail sets you can use Berserk off-CD but are bottle-necked by P6's jail set.

In regards to your question about Infuriate, let's go back to A5S. During earlier progression when people were using Berserk in their openers, due to the recast of Berserk finishing sometime around the first Boost mechanic, you had to hold Berserk until after the Boost mechanic in order to utilize its full duration (holding it here had no impact on your total Berserks throughout the fight so it was okay). As a result, you could afford to use Infuriate off-CD for an additional 5 stacks and still have it ready for your Berserk window after Boost.

The general idea I am trying to convey is that you want to look at the structure of a fight (duration / phasing / mechanics), determine how many Berserks you will get, and then optimize around that. There really is no definitive opener or rotation for WAR. There are just some general rules.

Never hold Berserk long enough to lose a Berserk in the fight.
Generally try to sync Berserk with at least Infuriate (ideally coordinate with your DRG/NIN to sync with BL/TA). Most will also sync with IR.

Fracture works in a similar way. I'll just quote myself from an older topic about it --

Quote Originally Posted by Brian_ View Post
Fracture delays your FC by 1 GCD every ~30 seconds.

1 GCD is worth roughly .67 wrath stacks due to heavy swing not generating any stacks.

Fracture costs you a FC once every ~4 minutes.

Over ~4 minutes, proper Fracture use will gain more potency than a lost FC. This gap only widens when the use of Fracture doesn't cost you an FC because of the cut-off in fight duration. For example, if a fight cuts off at 10 minutes, Fracture will have more value because the last ~2 minutes of Fracture up-time is purely a DPS gain.

But, like i've said here multiple times, there are conditions where Fracture is not a DPS gain.

1.) It forces an eye --> eye rotation instead of eye --> block multiple times. One instance of this happening is SE > Fracture > HS > FC > FC > SS > BB > HS > Maim > SE. Eye will fall off before reapplication in this rotation so you will need to swap SS > BB for Maim > SE instead. There are other content based instances where you might need to leave a boss for a GCD.

2.) You do not get the full duration out of Fracture for whatever reason.

3.) It costs you an FC in some very specific scenarios. For example, if you are Berserking near the end of a phase or fight and lose a Berserked FC as the result of an earlier Fracture.