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.

Depends on how the kitchen is and will be organized.

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.

Cabinets by Design LLC if there is no room there, where would you consider placing the refrigerator? I would need some dry area (counter top) as well to keep my mixer/blender etc. also some space in the bottom for cabinets to keep all those big vessels for cooking. How to make use of the corner portion well? side - d? I have to think about the possibility Sativa Jaeger Designs LLC mentuioned , about moving the kitchen opening up further north. I also don't want want the kitchen door to be just opposite to toilet door . the kitchen door should start at the point where toilet door ends. I know this is a huge challenge, as it is really small and thats the only drawback of this house which we had to compromise considering all other aspects.