It's just not feasible to regrout a mosaic tile floor because of the tremendous amount of grout that you'd need to remove. It is however, possible to retile over your existing ceramic tile.
But, before you do anything, is it possible for you to open an account at www.photobucket.com
or any of the other free internet image hosting web sites, borrow a digital camera and get a friend or computer geek to upload photos of your floor so that you can provide links to those pictures so that we can see it.
You see, I bought an apartment block about 22 years ago, and at the time I bought it, it was cheap because it was in very poor condition. Most of the bathrooms had deteriorated plastic tiles on them, and those that had ceramic tiles were poorly done and were covered in mildew. But, I found that I was able to clean up that mildew quite well so that those bathrooms looked quite nice again. And, I have since torn down all that old plastic and ceramic tiling and redone all of the bathrooms in new ceramic tile.
What I'm thinking is that if I could see the progress being made by your posting pictures of the floor after each step, it may very well be possible to restore the appearance of the floor to an acceptable level so that it wouldn't be necessary to regrout it. Or, failing that, to restore the appearance as much as possible, and then seal the grout so that it doesn't deteriorate from that level any further.