Cardsplain

The fine print

What counts. Tokens count when they are : , Axe and the Stone Boulder from Stone-Giant of High Pass. The 2/2 Dwarf tokens from Fíli and the 1/1 Human Soldiers from are neither, so they don't count. A creature that becomes an artifact counts while it is one, as when Stone by Sunlight's second mode saves it. Your opponent's never count for you.

When you earn it. You have an as soon as you control a card and two other pieces, even in the middle of combat, and the bonuses switch on at once. Óin the Brave can be the third piece and attack that turn with .

. Equip only as a , in your main phase with nothing on the , even when Dwarven Mauler or Kíli makes it cost . Vow to Erebor attaches an Equipment to a Dwarf at speed, and it isn't an equip ability, so Mauler's discount and Kíli's free equip don't apply to it. When the creature is returned to hand or (The Eagles Are Coming!, Celebrate the Mountain-king), the Equipment also stays on the battlefield, unattached. If the creature comes back, it is a new creature with nothing attached. Hone counters from Dwalin, Weaponmaster sit on the Equipment, so they move with it to the next creature.

Reminder text of Dwalin, Weaponmaster
Dwalin's reminder text says the is on the Equipment and grants +1/+0 to whichever creature wears it.

. Chapter I happens as the Saga enters. Each later chapter happens as your first main phase begins, after you draw. A chapter with no legal target does nothing and doesn't wait for one. The Saga counts toward storied until it is after its last chapter.

Chapters of Burn, Burn, Tree and Fern
Burn, Burn, Tree and Fern has four chapters, so its last one comes three turns after you cast it.