I think a comfortable distance between the island and the counter is around 42". It seems that you have only 30" between your cook top and the counter. I might be a little too tight. The wall between the entrance and the kitchen could be 4' long instead of 6', you would then be able to move the island a foot which would give you more room between the cook top and the island. Could you switch the location of the toilet and vanity in your dad's bathroom so your enter facing a vanity instead of a toilet which is a lot nicer.

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.

acc to ur kitchen cabinet pic, I would request u to get stone ( kadapa ) vertical base frame and on top before granite fitting and then wooden panel can be done for drawers n shelves. this will eliminate wood to get wet and start to fall apart. looking forward to modular version need to know it last few years only. wherever water is concerned only wooden panels won't work for longer n steady use. for counter tables or side working space that will work but not where the sink will be placed.

@corner Stone designs. sorry if I had given an impression it mud slinging. but objectively speaking the suggestion to go for a chimney just because someone asked for it instead of addressing the real issue us not what I intended to do. one has to understand all the negatives as well veggie going in for a decision . just like you have the right to suggest there is nothing wrong in pointing out the issues in the proposed solution. none of us are internet warriors but most of us are "sold" items that we will never need in our life by creating an illusion. I know that dinner call it business but I am not in such one and I have the luxury to call a spade a spade. Even now the person who asked for is not sure in what they want but they think that a chimney will solve the issue. engineering doesn't work that way. unless we know what the real issue us, which isn't clear if it is the smoke or the smell and the your of food cooked, the frequency, the 80/20 utility of the kitchen we are not even close to understanding the problem. my intent is to emphasize the importance of understanding the problem and then look for issue and not provide a ready made solution. we can all suggest something by seeing a picture that fire will come and catch the chef if it is located in the window but do you think that what you say is practical. you may construct this as much slinging be as a novice I have a genuine question. how many houses have such a fire accident. we don't even know if the stove is electric or gas. if it is electric then they just no question of fire. so I encourage you to objectively approach and not see this as a mud slinging thing as that's not the point.