Are you sure this is marble? And where is the flooring? Bathroom? Kitchen? Entrance? Is there a wear pattern to the black marks?

What was the stone sealed with? How long ago was that? How often are you resealing the product? What is your cleaning product and schedule?

Not sure about the sealing - I assume it was done at some point in the past. Is there an optimal sealing schedule?

Yes...and no. The sealing schedule depends on what the original product that was used. Are you the original installer of the floor or did you purchase the house with the marble in place?

And remember: marble is calcium carbonate. Calcium carbonate dissolves in the presence of acids. The more you clean it, the more you erode the surface. If this is pitting, then the daily cleaning is probably making it worse.

As for disinfecting, it is impossible to disinfect anything in a residential setting. The level of sterility required is only achievable in a clinical setting. And even in a clinical setting a floor will only reach "clean" it will never reach sterilized or "disinfected".

An autoclave is required to achieve sterilized/disinfected. The human biome requires biological INPUT so that it can create an accurate blue print for a healthy/high-functioning immune system. Only in medically rare situations is a "disinfected" household a requirement for a human being....like a person recovering from chemotherapy, radiation therapy or immunotherapy to control an autoimmune disease (like Lupus, etc).

We have some marble flooring in a bathroom. It can get stained (in fairness, I'm not sure that coffee cups belong in a bathroom :-) . If I had it to do again, I'd probably go granite or manufactured stone.
Read about pros and cons of marble flooring here