No you can not install granite, ceramic or porcelain tile over any type of tile. It needs to be removed and prepped for the new granite. If cement or concrete board is installed over the old granite then you can retile it without removing the original tile but there is no need. It is not a big deal to remove the old granite, you will be very surprised how easy it will come off. At 30 ftsq we are talking maybe an hour or two for 1 or 2 labourers with a chipping hammer on an average size fireplace to remove it. That seems to be a very high quote, however without really seeing the job it wouldn't be fair to the tile guy to dispute that quote. edit: I must add if the cause of the original tile cracking it will likely crack again. Is the quote include addressing the cracking issue as well?

Are the tiles installed horizontally around the fireplace opening? If they are, the spotting may well be from wood sap spitting out from the fire and landing on the tile. The spotting would be heaviest near the fireplace opening if this is the case. Should be relatively easy to fix by cleaning with paint thinner or similar product.

I know, you didn't ask about other parts of the room. The photos showing blue paint are nice, but I'd photoshop various transitional rugs. Seems a foundation would be better than wall changes. Soft blue imo is a tad delicate with much white. What about a soft teal, or green?

So we have south facing with a similar floor color, similar cabinets, and similar island (all of our bases are knotty alder stained mission oak, not just the island, but same idea). We chose Hanstone Paros Quartz counters which I guess lean cool but aren't super stark so they work with the warmth of the rest. Our backsplash is a chloe tile. We have extra white trim & cabinets. We chose SW Drift of Mist for the walls. I think it's a lovely color but it IS a color. Warm gray, that leans grayer in north rooms and looks nearly white in our south rooms. Trying to go lighter would've just looked washed out IMO. Here's what two similar whites look like next to each other. Drift of Mist on the walls. Kind of hard to see it in a photo, but it just looks off in person. This photo is also in a low light room so the DOM looks grayer. The color expert on this site (Lori Sawaya) mentioned in a previous post that if you want different colors between trim and walls, they need to be separated by a chroma of 0.3 (I think???) to not look like a dirty version of the same paint. Thankfully our contractor painted most of our stuff extra white (this was a happy mistake - we had chosen pure white) - I can tell that the one area with pure white trim (chroma 0.4) looks muddier next to drift of mist (chroma 0.6), while extra white (chroma 0.3) looks better. ETA Lori's color site if you want to poke around: https://thelandofcolor.com/