Quartz is man made, a resin. It can definitely scorch without a stainless heat barrier of sorts _ it resists heat to 100 degrees. . No you won't be able to repair it, should that happen.

I'd stick to the tile, in whites that mirror the dove of cabinetry.. It's also far better suited to the more basic range you're showing, which I assume has a microwave /venting above as in your mock up of materials AND the more organic/rustic feel of the terracotta. You're only going to have about 18 inches above the range exposed, IF you have the micro above. the tile will be lovely.

Your range manufacturer's installation instructions will dictate your backsplash choices. Start there please.

I used an interesting granite stone with some gray/white/green veining for kitchen counters, counter backsplash up to the upper cabinets and as the focal backsplash wall behind two gas ranges.

If looks like your range is LG and technically it requires 0 clearance behind it so that may reduce your chances of scorching the quartz on the backsplash but won't eliminate it.

I would potentially be concerned about the self-cleaning (which I know some people do not use). I used the self clean on the basic Frigidaire range currently in my kitchen and the temperature of the self cleaning discolored the enamel around the vents.

I'd prefer it with real stone as well. The faux stones are okay on the flat surfaces but not really something to show off on a wall. It's best to let them recede and be a supporting player.

I thought you only had to be careful with quartz behind the range if you have a gas OVEN…if dual fuel (electric ovens) you should be fine? Although we did not use quartz in our kitchen, our dual fuel range does not heat our tiled backsplash at all.

"I thought you only had to be careful with quartz behind the range if you have a gas OVEN…if dual fuel (electric ovens) you should be fine?"

Any heat source needs to be held at the proper manufacturers specified distance or use the manufacturers backguard.