Effectiveness is influenced by capacity of unit. If you are trying to mount a 270 cfm fan more than 30" above cooktop, then it may make noise but will do little to clear the air. If it is 1000 cfm, then it can be higher than 30". So the answer is "it depends". Most people don't mount them more than 36" above the cooktop unless it is a really high powered unit.

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A good tile installer that knows what he is doing, can easily remove that single piece of tile.... carefully replace it with another one. Do you have another extra pieces of the same tile? Do you know what brand and color the existing grout is? That will be more of the issue trying to get the grout match to match up or the finding the same tile (in the same dye lot) if you need to buy another tile. Did the heat cause the break or did a pan bang into the glass? Consider installing a heat resistant Lumicor or 3 Form panel behind the stove. Any flat material that can be sandwiched between two resin panels. 1). Crushed glass. 2). Fabric. 3). Fabric. 4). Fabric.

I would go with the second plan, more or less. Having a fridge right next to the wall seems like a bad idea to me, and I personally can't stand ranges/cooktops on islands--I like the hood venting straight outside. But I would want more countertop to the left of the fridge--when I take food out of the fridge I would want to plop it right onto the counter, and it looks like there's not enough room as it is.