My intuition and memory of Bonesplitter, MtG's most (in)famous axe, made me expect +2/+0.

I don't think, I can like this card without reminder text for Battleaxe.

Notice that the first triggered ability doesn't work intuitively since you need to announce targets as you cast the spell, so you need another target than the Battleaxe to begin with and actually change the target etc.

That's why Dwarven Hammer and co. work much better as Equipments.

"As you cast" might work though maybe an entirely new wording? "As you choose targets while casting this spell, you may create a Battleaxe token as its target."?

I'm not entirely certain the equip-altering ability works, but nothing off the top of my head prevents it.

Notice how the final ability only affects creatures enchanted or "equipped" by it, but doesn't pass on the ability to an enchanted Equipment. I solved that issue with inscribed abilities, but your wording doesn't create the necessary work-around.

What if it was “As you cast...” rather than “When you cast...” ?

I just read the rest of the card. It has other functionality too, not just the battleaxe part, so I guess it works out.

I mean, this has "enchant permanent", so the odds are pretty good that either you or an opponent will at least have a land to target. It means you can't cast this turn 1 on the play off a Simian Spirit Guide or Lotus Petal, I guess? (Actually, maybe you can cast it targeting the Lotus Petal, then sac the Petal to pay the mana cost? Tricky.)

This is weird, because you still need a legal target before you create the Battleaxe with the triggered ability. I think you should go with the Cloudform template, where this is a global enchantment that creates a token and attaches to it as an ETB

See Bloodlust Hexrune.

See Bloodlust Hexrune.

See Honorbound Hexrune.

See Bloodlust Hexrune.