I use water on my diamond plates, usually a weak solution of Simple Green. People swear by that for all sorts of things but I'm not entirely convinced it's that much better than a little dish soap or just water.

I tried window cleaner per Paul Sellers but didn't care for it. To be fair, he uses automotive window cleaner, which I didn't have and wasn't going to buy some to try it out, nor do I know if what he gets in the UK is the same as what we get in the US.

There will likely be rust on the plates, but know that is from the swarf, not the plate itself, which is a nickel alloy.

You can use a cheap rubber eraser to clean or one of those crepe sticks that are sold for cleaning sanding belts.

Diamond stones are pretty much fine with anything you want to use. In a pinch, use them dry but wipe off the metal dust frequently (dry rag). In the shop where I don't have a sink I use a spray bottle of isopropyl alcohol (50% seems about right). In the kitchen I use soapy water. I've seen oil used but I'd rather not have the mess.

Diamond stones don't absorb so any liquid that can be cleaned off and isn't corrosive or otherwise dangerous will work.