Why on earth would you play AP Volibear on tt or at all? Because it's simply insane in such close quarters that Twisted Treeline offers. Imagine a 3vs3 fight in which all the enemies have grouped in a situation like that just by landing basic attacks with your ultimate Stormbringer will already deal massive damage and easily win your team fights (if you aren't constantly CC'd). Generally volibear is not usually expected to deal a lot of damage but with this build you're kind of an unstoppable glass cannon.

On Ap volibear items like Nashor's Tooth and Lich Bane are pretty much all you need, I usually only buy these as my offensive items although Wooglet's Witchcap is a great item i usually buy it only for the armor/defensive traits.
1:
my recommended
If prefered over flash
2:
Only if contesting Vilemaw or counter jungle
Recommended
Recommended if your teammates have an ignite
Can work but I've found the other options better

21/9/0

The offensive mastery tree offers all you can possibly need: Attack damage, ability power, attack speed, hybrid penetration.

Everything you basically need from the defensive tree is: Damage Blocking and increased maxium hp.

There really isn't much to say about the masteries, overall pretty mandatory for this build. The utility tree is left untouched what could you possibly need from there? TT has increased mana regen + the 1.5% movement speed is pretty non existent after you get boots or an Aether Wisp, in addition you do not need cooldowns on summoner spells since they arent essential for engages.

Pretty much basic for an ability power reliant basic attack user
More Hp = Greater passive The Relentless Storm
i still use Greater Seal of Scaling Health over armor since Volibear's (W) Frenzy has immense execution damage with increased max hp, Greater Seal of Armors aren't as efficient because you can just buy an early Seeker's Armguard

Volibear can win pretty much 100 - 0 champions that do not offer massive damage (Burst), healing reduction (Grievous wounds) or Hard CC +(Attack speed reduction), but you will need to know what are your power spikes, basically Nashor's Tooth and Lich Bane are all you need for winning mid game fights.

breaking a fight (Make sure that you have vision of at least 1 absent member of the enemy team)

Initiate with your (Q) Thundering Smash for an easy bursty Lich Bane proc, additionally this will already give you a stack of Frenzy . Use your (E) Sky Splitter for the slow and huge aoe magic damage, after that start smashing them in the face with your (R) Stormbringer every basic attack will start dealing outrageous magical damage. Once they are low your (W) Frenzy 's active will deal a significant ammount of damage surely able to finish them even from a slight distance.

So in a team fight you're pretty much a squishy assasin, but after you buy a defensive item ( Wooglet's Witchcap, Randuin's Omen) then your team will be able to destroy enemies that focus you.