For what it's worth I've had bits of oil on a couple of more stones in the past, and it hasn't mattered really at all aside from initially being an annoyance, and then after a bit of diamond rubbing or time the oil spot would disappear. I'd guess that, unless you're a really subtle skilled razor sharpener, I don't think any knife sharpener would notice changes to the slurry if you had a small oil mishap.
Density/structure - I think you can use your common sense and figure things out when you have a new stone most of the time. Kyoto finisher-type stones are going to be layered and that is their general structure, unless in you're in suita territory with the crazy lines. Aoto are layered perpendicularly. Not many other layered stones out there. Of the many potential rest, you've got to think about how they feel (you can tap them, feel them, notice their sound and response when sharpening..) and you can get a feel for their density and how 'together' they are maybe also on a finer level, and if they'll react pretty uniformly to water or not. If not, then the stone might be less stable and bits can break off or a fissure can appear. Sure lacquering is good, but lacquer will also penetrate in and force open small cracks and generally challenge the more exterior area of the stone when applied, I think. When you get past that and the stone's survived then you'll be better off. Some stones seem to get lots of surface cracks too, but they don't seem to penetrate in a threatening way they seem just be part of the personality of that stone
About leaving slurry on stones, I think this is done a lot. Saves you from generating new slurry next time, looks a bit messy yes, but can be more convenient and lessens wear and tear. Thinking of rust, one of us can speak with a Chemistry grad or a geologist or someone, perhaps, that could tell us more about the PH, etc, that we might be working with and how the type of water you use, the steel and stone all react together, and that could be useful. I've noticed how if you have a reactive knife and get a bit of water on it you'll get the rust, but then if you are busy sharpening that knife for a while and it's in contact with plenty of water + slurry (not sure about synths so much) it seems that reactivity is low or pretty unseen. Hmm, thinking of it some nats seem to discolour a bit from use, so there's a bit of brownness due to rust/oxidisation, but not usually. They'll all have different properties but it's hard to guess and know unless you try things out and get to know the stone and how it does with what you use it with.