— 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.

Only between levels and only before you pick up a perk. The altar gets destroyed after this and you can no longer edit your wands. But like superBlast said, there is a perk that lets you edit your wands everywhere. Well.. Thats hard to say. You get gold and stuff if you explore the levels as much as possible but chances that you get yourself killed are very high. I once rushed through the levels and encountered some kind of a boss monster. You have no chance without a proper equipment. The staffs you can purchase between the levels get more and more expensive, so I highly recommend collecting as much gold as possible. That requires you to kill as many monsters as you can and / or dig for the gold in the first 2 levels. I recommend getting stains of water and / or blood on you as often and as much as you can. Sure, you won't be able to benefit from invisibility or the stainless armor, but it prevents you from catching fire. The stains will vanish just by walking around, check the remaining percentage with your mouse on the symbols on the right. You should also carry around at least one bottle of water to clear toxic waste and clean yourself if needed. Most of the time I lose my health more from fire, acid or toxic, not so much from enemies, at least in the first levels. Later in the game the enemies will be much stronger and are the bigger problem.

Unless monster infighting blocks that off I can't say I can confirm this, at the very least for the mines. Though in one out of 3 attempts just now I've had a chest spawn on the perk podium with a spell inside (that "turns everything in a short radius into oil, including walls, creatures... and you" (couldn't test it since it needs 260 mana per cast but wtf !?)) but I couldn't say whether that chest was spawned due to the seed...

I think the altar is only destroyed if you walk to the right. You can pick a perk and walk left and still mess with the wands or shop.

You're right, the altar gets destroyed after you walk past it (under the exit "door").