Plumbing – Why can’t the plumber fix the kitchen sink

Put on good rubber gloves, preferably ones that are made for handling hazardous chemicals, and safety goggles.
Make a thick paste with a cup of baking soda and cold water and spread it over the area to neutralize the sulfuric acid. Even though it has dried it is still active. Let the paste sit for 10-15 minutes before touching it. You may want to open a nearby window as this can release a fair amount of CO2.

Using a 2 inch or larger putty knife, carefully scrape away part of the baking soda to reveal the counter. Next carefully scrape at the edges of the spill. Keep doing this until all of the baking soda is gone.

I can't tell from the picture if your counter top is a type of laminate or granite. If it is laminate you may find that the "cement-like material" is actually your counter top and the acid has melted it. If it is granite you may need to have the counter professionally polished to get rid of the stain.

Best of luck

Usually it is illegal for the landlord to charge for building repairs. The only time a landlord should be able to charge is when the damage is not from normal wear and tear (like dumping a pot of rice down the garbage disposal).

It's hard to guess what is causing the blockage but bet it is related to the Nu-Flo coating de-laminating and clogging the drain. It is best to notify the landlord to have a plumber come out to auger the line.

The item on your sink is an 'air gap' to connect the dishwasher to the disposal. The air gap prevents the garbage disposal from black flowing into the dishwasher.