ill answer treps Q fisrt, because its easier

i use treated tap water. to treat it i use repti safe water treatment. most of the time i make a bucket at a time and let it sit out for a day or two before use. ive treated water then put it imeediatly into a tnka though, without incedent.
B-R-F,
water is a neccesary part of vivariums, but can be present in many different forms. there are tanks with no visible water surface, but they still have some sort of standing water in the dranage area. there are tanks that only use mist and the settling water is drained immediatly, but these types of set ups arent common and need lots of misting. there are tanks that are set up with no moving water, but do have a pond type feature with standing water visible and excesible. the most elaborate set ups can include waterfalls, moving rivers, drip walls, and misting systems.
in all of these types of systems the most important things are the water level, and the water quality. the water level is important because you dont want it rising up into your substrate and rotting away your soil. this fouls the water, but more so will rot the roots of terrestial plants and create bad mold an fungus problems.
water quality is one of the easiest things in a viv, if you dont have fish. if you try and include some type of fish into your viv, you need to treat the water section as if its a regular fish tank. the fish still have the same requirements, and filtration becomes more neccesary due to the fish waste. filtration should be then based on water vloume and fish load, exactly as it would in a conventional aquarium.
without fish a bacteria load will be formed and will generally take care of any FFs/animal waste that make it into the water, and will generally keep the water plenty clean for any herps that would make use of it (discluding some of the more aquatic species, as they would requir esome additional filtration).
if you frequently mist and have tight fitting lids, youll generally need to take water out on occasion. this is simply the build up of mist. in essence your are changing water every time you do, albiet over the course of weeks or months, but its still ususally plaeny effective (100% IME).
ive had tanks set up in all the manners stated above. with proper planning/equipment you can do any of them rather maintenance free.