Google limestone cleaning. There are many things you should not use on limestone. I know you are interested in cleaning the grout, however, you need to know what to not use on the limestone. I have no clue what Finish Power Ball dishwasher detergent would do to limestone, it does clean grout good by soaking/scrubbing with stiff grout brush. If very dirty, will need a repeat or another repeat. I have cleaned several rooms of grout/porcelain tile with good results using the above. I do need to repeat the process again and again if necessary to get clean enough to put a sealer on the grout. All depends on how dirty the grout is. Most hand grout brushes require too much muscle power to use, buy an "Unger" grout brush, the grey one from a janitor supply place. Put brush on handle of desired length to scrub. The brush is about 8" long and beveled, fits in the grout line just right to get maximum scrubbing. Think the Bristles are nylon and are very, very, very stiff but do not scratch the tile. For floors I put a long broom handle on the brush making it easier to scrub standing up.

If cleaning the tiles with Tilex is a one-time thing, you can do what I did. I used tape and plastic to cover my fiberglass shower floor while I applied StoneTech Restore (a highly concentrated acidic cleaner) to the tiles on the shower walls. Regarding the limestone staining, go to the John Bridge Tile Forum's Cleaning, Restoration and Sealing forum and post your question there. Maybe there is a sealer that can be applied to the limestone. Here is a link that might be useful: John Bridge Tile Forums

I happen to like limestone. It certainly has places where it should not be used, as it's soft, can scratch, and the scratches can hold and show dirt. So a floor in a food court at the local shopping mall may not be the best place to install it. But it's a great decorative stone, and wonderful for residential use. Mongo

Home Depot has a pretty good selection its not with caulk its with the grout, usually. Look at the big ends of the tube usually some has smeared and dried, there you can get a good idea of the final color. You should be able to get something that will go nicely. To keep it from smearing into the grout on the wall i put a strip of blue painters tape along the wall about 1/8 " away from the joint. I prefer thinner caulk lines you could go a little further away if you wanted a wider line.