The ally Carbucle says to recharge it to explore. If a monster, shuffle it into an open location instead. Was he ever really recharged?
I'd say no. You did something else instead of recharging it, so you never recharged it.
Lann allows you to pull a weapon from the the box to use for combat. It will be banished at the end of combat. I recharge that weapon. Does it still get banished from the bottom of my deck?
It never goes to the bottom of your deck. Use the powers on the card, but then just banish the card. See this FAQ.