Mutilate is useful when the enemies health is high enough to for the entire duration, otherwise, yes, the potency may be good enough, but you could just as quickly burn without it and fit in other useful combinations. Sure, 5 ticks will equal a gust slash... but in that 5 ticks, you could of gotten a spinning edge AND a gust slash through and you're close to getting an Aeolian edge off too. Low hp trash mobs could easily be taken out before you get any real use form that mutilate. Not to say it isn't useful, but not on low hp trash. Kinda like fracture for WAR. It's usually worth it to get something else in if the fight's not gonna prolong. Shadow fang should be prioritized though.
As for your statement, no, shadow fang should NOT be the first thing applied after TA. It should already be applied if it's a boss along with DE's debuff prior to TA being used. If you set off TA without those already applied, you are already losing out on DPS opportunity (unless you have a WAR that applied storms edge debuff).
I will say, my above rotation that I actually wrote out was specifically for higher hp trash, so my mistake saying it could be used on bosses. That should not be looking over it again. I made the statement without thinking through completely on that one. Boss rotation for me would be:
pro huton prior > poison on > mutilate (only because it has longest duration) > SE > GS > DE > SE > SF > SE > Suiton > GS > TA >Duality with AE > DwD > Jug > Mug > SE > GS > AE (TA should ending about now).
If a WAR is my Tank, then I can speed things up and skip the DE combo. By no means am I saying this is the end all only way to do this. I find i'm comfortable with this rotation and it works well for me.
yes, prioritize keeping huton up. Me personally, I wouldn't redo my NIN at 30 seconds left though... that seems a bit wasteful to me as you could literally get another ninjitsu in 20 seconds (which gives you an additional 10 seconds room as well for fitting other things in before needing to redo it). With armor crush, then yes, I will use it around 30 sec, but not ninjitsu.
If you know the mob is going to take a while to burn down, then use Doton. If it's going to be a quick mob clean up (like if your tank only pulls 1 mob at a time) katon is more likely your go to. When you get kassatsu, use both. Suiton should be used after applying your DOTS and debuffs onto a boss to use it in the middle of a fight. You can use it on trash as well, it'll burn through an individual trash enemy extremely quickly if you all focus on the enemy appropriately. Just make sure to have TA available again for a boss. Hyoton... only if you need something to stop moving. For PvE, this is usually only an issue in terms of stopping an enemy from chasing you so you can get some extra time in. Raiton should be used often on single targets. Bosses if your TA is on cooldown.