I researched this pretty thoroughly when I got my new laminate flooring a year ago and using a steam mop on a laminate floor is asking for trouble. Experts will warn you away from that. And, for mopping, you should never mop it like you would a tile or vinyl floor where it doesn't matter the amount of water you use. I use a laminate cleaner made strictly for laminate (not real wood) and a microfiber or terry cloth pad. There is only enough liquid to remove the marks, never more. And, of course, it is vacuumed first to remove dust and dirt because the biggest enemy of laminate is to capture the dirt and then scrape it across your floor while cleaning. Wet Swiffer products are probably not a good idea either because they introduce solvents that will haze and detract from the nice finish of the flooring. And, no Murphy's oil products...they are great for real wood but will cause a smeary mess on laminate. The Bruce products are great and so are the Abbey floor cleaner products. I would love to hear if someone has tried the BonaKemi products because the refillable floor mop system seems interesting.

I second the power washer. If you don't have one I think you can rent them, but they are a worthwhile investment. I have a lot of pots on my patio. I wash it with the hose when I'm finished planting but the whole patio gets grungy over the summer. Every spring before we bring out the patio furniture my husband goes over it with thw washer. It not only gets the grunge but any moss that happens to be on them and we have a like new patio.

The best way to clean furniture for painting depends on the current finish and condition as well as the desired finish. If you only want a distressed paint finish you may not need to be as thorough as if you want a very fine smooth painted finish. If the piece is really dirty I have used Murphy's Oil Soap or TSP, rinsed with the hose (on the patio!), and dried quickly with old terry towels. Then let the piece dry for another day, sand if necessary, and stain or paint. When DH painted our kitchen cabinets he used mineral spirits which removes grease. For an alligatored finish you can use denatured alcohol or laquer thinner to remove shellac or lacquer. Sometimes with old pieces there are years of wax imbedded with dust and dirt which needs to be removed or the paint won't adhere and mineral spirits or denatured alcohol will remove that. It's necessary to use good gloves and work in a well ventilated area as the stuff is quite toxic. There's a product called "Citrus Natural Solvent" I'd like to try as it's supposed to be more environmentally friendly than other products.

The only way I know to safely restore the stone is to have it refinished. You may want to check other sources for refinishing as it's only a few hours work. If you have a hard time finding a reasonably priced company, perhaps you'll have luck asking who does the work in nearby churches, hotels, hospitals etc. If their referral is a long-time in-house maintenance staff, perhaps you can negotiate with him directly as a side-job if it seems safe to do so. Some installers do this repair as well so that's another potential source instead of the franchise refinisher I think you may have gotten the quote from. You won't necessarily have to have it honed as, if it's not too far gone, they can use a solution akin to tooth polish and buff. If it needs to be refilled and honed, that's only a bit more complicated but should be doable in a day's work. You can clean it with a steam cleaner but you may wind up taking out more of the fill. Do not use any citric based solution if you try. I don't know of any good DIY treatments for bringing back the shine, but once it is polished, be sure to maintain with the right ph balanced cleaners. Maybe others will chime in here. You can also ask in the flooring and kitchen forums as some knowledgeable stone people frequent there. Good luck!