I have done a DIY repair on similar by using permanent marker to just hide the lighter colouring that is showing. Otherwise sand it down and refinish it.

It’s not possible to sand it’s a stone , unless I find someone who works with the stones

Overlapping dots of black and brown sharpie would make that disappear.

I think I need some filler to fill in the cracks in the stone

If it is real stone, then you should be able to sand the mitered edge and round it off ... first check that the mitered waterfall isn't starting to separate.