The 50-yr-old hex tile in my bathroom didn't weather our remodeling project too well. Because this bathroom was one of the few rooms left untouched, it was used as something like a utility closet for the duration.
Now that the crew is gone, I can see this use didn't go over well with my old tile.
I've been using a razor blade to scrape off what looks like drips of stain or polyurethane (they refinished some woodwork in there, but apparently didn't use a dropcloth). But how to get the splotches of dripped grout off? That's not coming off with my blade. Also, the whole thing just looks really dingy and stained. It never looked perfect, but the imperfection was of the "gives it character" sort. Now the imperfection is of the "wow, do you ever clean your floor?" sort.
Any ideas?

This is often a difficult project with all the grout lines and the small tiles. The only way to remove the stains from the grout is to remove the grout itself. There are companies that do just this type of work, or at least depending on the area in which you reside.

IF not you can do this time consuming project yourself. A high speed rotory saw found in most home centers with a grout removal bit should do the trick. This is a very dusty project so be sure to open the window and close the doot while doing this. A window fan is also a good idea to draw the dust out. Do not forget to put a fan in window to pull the dust out as well.
Take your time and you will be able to cut out the grout where needed and then before you regrout where you removed offending material. Clean the old left over grout with a good grout cleaner found in most tile shops. This cleaner should brighten up the old so the new clean stuff will blend in better.

I am adding an upstairs master bath in a small room connected to the master bedroom. There is a wet-wall containing plumbing for an existing upstairs bath and existing downstairs bath. The existing upstairs and downstairs toilets each have their own wastepipes to the main drain in the crawlspace. Can a new toilet connection be added to the vented vertical wastewater pipe that serves the downstaires toilet or would this be a no-no? If not, can a 2-way toilet arrangement (one on each side of the wet-wall) be installed on the vented upstairs vertical wastepipe?

A back to back toilet is very common, yes you can do this as long as the vent is properly sized.