Over the years working in QC/QA, I have used just about everything for cleaning plates. From Windex type ammonia cleaners to MEK. And lots in between. Probably best all around is Fantastik or Formula 409, lots of paper towels and a good rinse with clean water and more paper towels. This will generally be sufficient unless there are marks left by solvent based agents. Then out come the tough stuff, like Toluene, Xylene, and MEK. PLEASE TAKE PROPER PRECAUTIONS if you have to use any of those. Extremely flammable, toxic and carcinogenic. But there isn't much they won't remove. And they leave the plate very dry, and that has always been my preference. I worked for an older guy once you wanted me to use GoJo, and after I cleaned it my way, I did....looked very nice, colors in the granite showed nicely, but I really never liked the lanolin residue.
As far as the dust goes, if you have the plate in an open shop, you can hardly stop that. That's one reason I asked about a cover. Not really a nice wooden top like you are doing, but I was thinking of something just to keep it clean. Yours will do that as well. Dust is your enemy though, so you should wipe it down before you use it. That's about all you can do in an open environment.
Realistically, being level is secondary (by far) to having it certified and lapped flat to whatever specification needed. Or at least lapped. In a home shop, a cert isn't all that useful, unless you do commercial work where you have to keep records of all calibrations. Granted, having it level makes some things easier, but it isn't absolutely necessary. And 0.0002/12" should be more than adequate. And if it's on casters ad gets moved, that's out the window anyway.
hew: Didn't break a tap either!