— Can spells be added and remove from the wands only between levels?
— Should the levels be explored fully or is there a benefit to rushing?
— How do I remove water stains? Or all other stains without having to submerge in a different liquid.
1) Yeah, although if you are lucky you can get a perk from one of the inbetween areas that let you edit wands anywhere.
2) Personally I try to explore as much as I can until my HP gets too low. Rushing is safer although I'm sure you'll run into trouble in the later levels if you don't collect gold, wands/spells, and flasks. Exploring lets you get more stuff but increases your chances of getting into a really bad situration.
On that note, I think I heard somewhere that you would be rewarded gold if you get through a level without killing anything... though haven't tried it myself so take my word with a grain of salt.
3) Fire (unless it's oil). If you can use fire to dry yourself off and when you get a low % you can just run around the rest of the time to get rid of the rest. Although a much safer but slower methed is simply don't enter any liquads for a while. You'll eventually dry off on your own. That said, Blood and Water stains are 100% beneficial to you unless you grab certain perks. Though if you still want to get rid of stains, there is a perk that'll get rid of them much faster just by moving but it will get rid of beneficial stains as well.