[Spoilers] 3 Spears+0-cost items, buffing AOE abilities

So the 3 Spears can >!recover items based on their cost!< - how does this work with items that have no cost? Do they automatically get restored? How does this interact with the solo scenario item?

In addition I'm wondering about AOE abilities and buffs. I've been playing this entire time treating an AOE attack, such as Heatwave (on Spellweaver) as one attack, so buffing it with the bow for example means all hits have advantage. Is this incorrect?