It would not count an arrow, in part because the arrows burn themselves up.

As for dropping the sword and running to a new map, I didn't know that was a thing, like, I thought if someone challenges you to a fight, you load up a virtual space for that fight and fight. If you leave you're forfeiting and lose, I thought.

As for someone holding the weapon, that would be fine, but to teleport to it, there would have to be space for her to be, so if they stow the weapon in a backpack, Ronin can't teleport to it.