When it comes to what actions to take post-spellwork, I always suggest checking the spell instructions first. If the spell instructions do not specify what to do, then I say it’s up to you how to handle spell remains and used tools 
Like Megan said, perishable or natural ingredients can be disposed of in various ways (burying in soil, burning, releasing into the wind, etc- while being mindful to be eco-friendly with disposal). There was actually just an Offerings Challenge where people shared how they dispose of offerings post-spellwork- you could check out their challenge entries to get some ideas! 
When it comes to used magickal tools or accessories (such as a handkerchief), I’d say it is fine to cleanse the tool in question with your preferred method of cleansing (salt, sage, smoke, moon light, etc). After it is cleansed of the energies of the past spell, you should be fine to use it again in future spellwork 
Others may have different interpretations about this, but I’ve always found sleeping near my tools (such as my tarot decks) to help me bond with them on a deeper level. Personally, I see it as helping them to connect with the deeper levels of consciousness which open up during sleep 
If you’d prefer to keep your box in an open area, I’d say that’s fine! It sounds like you would be replacing the sleep component of the spell with time charging in the moonlight, which is another wonderful way to charge the spell.
Again, there are some who might disagree, but I think (unless the spell specifically says not to alter anything) it is totally fine to add or substitute ingredients to customize the spell to best suit you and your needs 
Good luck and blessed casting!