Waterstones for kitchens (watery environment), oil stones for woodwork shops (dry environment). Though you could use either of course, if you had to.
You haven't got a clue what you're talking about. The most popular device sold for knives is a tri hone - an oil bath, like Norton's IM 313. It's only been aimed at woodworkers recently. The stones kitted with them are designed entirely for sharpening knives intended to be steeled - not for tools.
The use of waterstones historically didn't involve a faucet, it involved a bucket. Cleaning the stone is as simple is dipping it in the bucket and wiping across it once. You managed to dance past the coticule thing again, an extremely common bench and site stone - often used with spit - graded for various uses by characteristics, from knives to tools to razors, with overlap. It's possible to use oil on them since they're generally pore-free, but far more common to use water or spit.
it doesn't do anyone any good when you make absolute statements and then claim experience - people just getting into the hobby may believe you until they've been around here for a little while.
Information about stones is publicly available now, and it was publicly available 150-200 years ago in holtzapffel's publications, both with types of stones/lubricant and their use.