How do I fix a recurring sinkhole?

I have an area where my driveway, front walk and a shrub bed more or less meet. That area is sinking. It did this before, and our landscaper attempted to fix it by paving. Do you have any suggestions as to what is needed to repair this?

My second question is regarding my brick fireplace. It is stained with white, which I know is not uncommon. Do you have any simple cleaning instructions for it?

Particularly since it has sunk twice, I think the area is a sinkhole, which is common. It can happen due to natural voids in the earth under the surface. Or the builder buried old trees and wood scraps there, so when the wood rotted, the void occurred. Or underground water caused the gap. The only cure is to dig down to see if you can find the void, taking precautions against collapsing walls or further sinking. Fill the void, tamp it thoroughly, and wait awhile to see whether any more sinking occurs.

As for the white stains on the fireplace, that is efflorescence, the leaching of lime from the brick or mortar. It is harmless, and you can get rid of it with a solution of half water and half muriatic acid. Please heed all safety precautions on the label.