A-h-h-h-h- THE OLD ACID TRICK.
Acids are so misunderstood and in some cases dangerous to use and yet people continue to suggest acids without knowing a damned thing about them.
Acids that would be used to address issues with masonry products WILL NOT HAVE ANY EFFECT ON DIRT. That's not how acids work.
Use any houshold cleaner to clean the tiles. I would suggest Spic-N-Span.
Then the grout is another issue. If grout is cracking in areas then there is a problem with either loose tiles or structural movement. In either case simply regrouting WILL NOT resolve the issue for very long. The grout will crack again.
Should you decide to regrout and live with the expectation of doing it again down the road then remove all the grout and start over. Using a modified grout will help expand the life of the grout to a small degree.
Aqua-Mix products are top-o-the-line products.
Once the tile is cleaned and the new grout is in place then seal everything abundantly with a stone sealer such as Aqua-Mix.
The thing to do is to get to the bottom of what is really destroying the grout.
Are there loose tiles also? Is this a wood or concrete floor under the tile?