How do you know its 3"? I have no idea what range that is. Is it a sealed burner; an open burner: what are the btu's?. They all have different installation guides. I know I've read many of them. They range anywhere form 1" to walls above the countertop for the old fashioned open burners to 12" for the newer sealed burners. See Fisher and Paykal here: http://www.ajmadison.com/ajmadison/itemdocs/OR30SNDGX_installation_instructions_and_user_manual.pdf The most common seems to be 5-6". Premier ranges for example all require 5" to combustibles less than 18" above the countertop, even if the range has 4 9k btu sealed burners, Yet Maytag and Whirlpool have many ranges with 2" clearances to combustibles; many of which have up to 15K sealed power burners. Kenmore also. Kenmore has a chart 9-15k 2" and it increases from there based on burner size. To make matters even more confusing: Maytag guides say follow range hood instructions for clearance directly above the range; yet GE for a very basic 8 or 9k open burner model requires a minimum 24" above the cooktop if a range hood is installed. OK. I've found a few Broan range hoods that specify installation 18-24 in. above the cooktop for optimal performance. So which guide does one follow?

In "A Pattern Language" which is a book about architecture, Christopher Alexander the author speaks about using smaller windows on view walls. The reason for this, according to him, is that when one constantly sees a view through huge windows it becomes so commonplace that one no longer really sees it. He recommends using smaller windows so the view is glimpsed in smaller increments and appreciated more. So IMO using the fireplace to block part of the view is not a mistake altho I think it could have been done more esthetically. The fireplace IMO has too much contrast to the white walls and is really not as special a choice as might have been made in what is likely a very expensive home. Overall I think it's a pretty 'blah' room and not a great advertisement for the designer but that's just my opinion and likely because it's not my style at all. Here is a link that might be useful: A Pattern Language

"I don't see it as a hazard." This is why the building codes are to protect you, from you. "(B) Protection from Physical Damage. Cable shall be protected from physical damage where necessary by rigid" In residential applications where there is a potential for damage from otherwise normal occupant activity. Locally, wiring in garages must be encased in metallic conduit to a height of 8' above the floor. In chicago, everything is in conduit. Generally, it's common sense that on the exterior the potential for damage is a given. "Where passing through a floor" Walls get moved, accidentally and on purpose.

Some of my info will repeat what has already been written. In the first photo: It looks like the duct is looped around to go behind the fan and then it goes up to the roof to exhaust. I would have rotated the installation of the fan housing itself to give a shorter path to the exhaust boot. 2) Rigid duct is better than flex duct. The wire coil in the flex offers more resistance to air movement through the duct resulting in your fan moving less air. 3) Insulate the duct for less chance of moisture vapor in the duct condensing and pooling in the duct, or running back into the fan housing. 4) It looks like light can be seen coming from the bathroom below. If so, the fan housing installation is poorly sealed to the bathroom below. Seal those gaps/holes, either with canned foam or aluminum tape, etc. Free air movement between conditioned living space and unconditioned space is bad for myriad reasons. See the dark/discolored/dirty fiberglass insulation? That discoloration is usually a result of the fiberglass insulation acting as an air filter. The discoloration is from the fiberglass filtering pollutants put of the air as air flows through the fiberglass. The second fan: Comments remain the same, with one addition. Since the duct is longer, when you replace it with rigid duct, have the duct leave the fan and run it vertical to a height a couple of inches above the height of the gable wall's exhaust boot. Then as it runs horizontal to the exhaust boot, pitch the duct downward a bit. That way if there is any condensation in the duct, it'll run out versus pooling in the duct.