Just to clarify, you have presented 3 versions. I believe the consensus is the original version with the wood grain ( linen grain) cabinetry works the best and is most updated. The only thing that is out of place are the cabinets or "shelves" on both sides of the range hood. If this is what you need to find a solution too. I would suggest only experimenting with rendering options for these two cabinets( or shelves). This cabinet ties in all the other hard surfaces. The white is not working. It just adds another element. The black is a little dated.

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.

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.

Usually when you get side panels you automatically have space on the sides. If you have a full depth cabinet on the top, you automatically have space at the top and in most cases you will have leave at least 1 inch of extra room for the back of the refrigerator, so there is always air circulation since everything is enclosed. In the 70's they use to make a small recessed space behind like Fred said, today you don't have to do that, most Ref have flat backs, recessed wiring, not to mention the supply for ice-maker also comes in a flush mounting kits for the wall... so pretty much everything is recessed and only space you need is for air circulation and 1" is more then enough. In addition, if you make recessed area now and you push ref to far you will never get your doors open so doing all that is a waste of time, in addition most manufacturers starting to make 30" side panels.